This is a very good and interesting question. Actually, Draupadi is a very important character in the Mahabharata. She was the direct incarnation of Bharati devi, the wife of Lord Mukhyaprana Vayudeva.
WHO IS BHARATI DEVI AND SRI MUKHYAPRANA VAYUDEVA?
Bharati devi, is the wife of SriMukhyaprana Vayudeva. Lord Vishnu at the time of creation, expanded himself into 4 forms namely : Vaasudeva, Sankarshana, Pradyumna and Aniruddha. Even Lakshmi devi expanded herself into 4 forms : Maya, Jayaa, Kruti, Shanti respectively. These are known as the Vyuha roopas of Lord Vishnu and Goddess Lakshmi. Now, from Vaasudeva and Mayadevi came Chaturmukha Brahma. From Shantidevi and Aniruddha roopi Narayana came Saraswati devi. Both Brahmadeva and Saraswati devi were married.
Now, Chaturmukha Brahmadeva prayed Lord Narayana that he wanted someone who could help him with the creation and would be equal to him (Chaturmukha Brahmadeva). Lord Sankarshana roopi Narayana, wished to have a son, who is very powerful, intelligent and is equal to Brahma and is very much high and superior in devotion as compared to other jivas. So, from his four hands came SriMukhyaprana Vayudeva as : Dharma, Vigyaana, Vairagya and Paramaishvarya. Since he came from Lord’s four arms in four forms, Lord Mukhyaprana Vayudeva is the embodiment of these four gunas. This comes in the Maandukya Upanishad.
Now, from Krutidevi and Pradyumna roopi paramatma came Bhaarati devi. SriMukhyaprana Vayudeva and Bharati devi were married. Hence, SriMukhyaprana Vayudeva is equal to Lord Brahmadeva and SriBharatidevi is equal to SriSarasvati devi. SriMukhyaprana Vayudeva is the presiding deity for breath and life force. Without him no jiva can exist. If the presiding deities for ear, eyes, nose or mouth leave the body, then that person might be known as deaf, blind or dumb. But he is still alive. But if SriMukhyaprana Vayudeva leaves the body then, that person is no more a person but a corpse. Even if the presiding deities enter this body again, the body won’t be functional since, the main deity Mukhyaprana Vayudeva is not present. If he enters then other organs can work. This Mukhyaprana Vayudeva, the son of Lord Sankarshana and Jayaadevi came as Hanuman in Tretayuga, Bheemasena in Dvapara Yuga and SriMadhvacharya in Kaliyuga. SriMukhyaprana Vayudeva is also known as Jivottama due to his causeless devotion in Lord Narayana. SriMukhyaprana Vayudeva is present within every devata, human, demon, animal, bird, every jiva. Everything is in control of SriMukhyaprana Vayudeva and he himself is under the control of Sriman Narayana. He makes us breath every second and does Hamsa mantra japa sitting within us, thus making us breathe. He is present in our sushumna naadi praising Lord Narayana with the Omkaara chanting.
Now, coming to Bharatidevi. Bharatidevi is the presiding deity for pure knowledge along with SriSarasvati devi. Bharatidevi is also Vidyut abhimaani devata which means she is the presiding deity for brilliance and light. She can make a dumb an excellent orator, a moron or idiot into a highly intellectual person. She is also known as Vaagdevi (the goddess of speech) along with SriSarasvati devi. As per Shatprashna Upanishad, Mukhyaprana Vayudeva has his sannidhana in Surya in day whereas Bharatidevi has her sannidhana in Moon at night. They are referred there as Rayi-Praana (Bhaarati-Mukhyaprana).
[SriBharati devi, the wife of SriMukhyaprana Vayudeva]
Draupadi devi is the incarnation of this Bhaarati devi, the wife of SriMukhyaprana Vayudeva. Now, why did I tell you all this? So, that this remains a stage with all basics cleared for reading further.
NOW WHY DID DRAUPADI HAD 5 HUSBANDS?
As per Garuda Purana and SriMadhvacharya’s Mahabharata Tatparya Nirnaya, there is a reason why Draupadi had 5 husbands. The reason is her Panchapatitva. Earlier an incident happened. It so happened that, once Lord Brahma called a sabha wherein the devatas along with their wives went. There what happened is, Yamadharmaraja was sitting with Shyamala devi, Indradeva was sitting with Shachidevi, Lord Shiva was seated with Parvatidevi, and the Ashvini devatas were sitting with their wife Ushadevi. Now, Shyamaladevi, Parvatidevi, Shachidevi and Ushadevi were expressing intense mutual affection and passion with their husbands inside the court or presence of Lord Brahma. This display violated the strict decorum and spiritual discipline required in Brahmaloka.
Lord Brahma was angry with this behavior and hence cursed Shyamaladevi, Parvatidevi, Shachidevi, Ushadevi to take birth as mortals on earth. Now, they prayed for a solution. So, they seeked refuge in SriBhaarati devi. SriBharatidevi gave them place in her own svaroopa as Draupadi devi. Draupadi devi was actually SriBharatidevi only, but there were even Shyamaladevi, Shachidevi and Ushadevi within her. So, there were 5 people within Draupadi - mainly Bharatidevi, then Shyamaladevi, Parvatidevi, Shachidevi and Ushadevi.
They followed a system wherein whenever Draupadi interacted with a specific Pandava, that particular devi associated with the Pandava would rise up and would be active in Draupadi. For example, when Draupadi was with Dharmaraja Yudhishthira, Shyamaladevi was active in Draupadi and rest were inactive. So, Dharmaraja being the incarnation of Yamadharmaraja, Shyamaladevi would be with her. When Draupadi was with Bheemasena, Bharatidevi would be active. Since, Bheemasena is the incarnation of SriMukhyaprana Vayudeva, Bharatidevi would be active within Draupadi. When she was with Arjuna, Shachidevi would be active within Draupadi, since Arjuna was Indra incarnate. Similarly when she was with Nakula-Sahadeva, Ushadevi would be active within Draupadi and rest would be inactive within her. So, in this way, Draupadi had 5 husbands with 5 goddesses within her.
SCRIPTURAL PROOF:
GARUDA PURANA
श्यामला भारती चैव शची चोषा तथैव च।
उमा च पञ्च देव्यस्तु द्रौपदीं संश्रिताः सदा॥ ४॥
तासां तु भारती देवी मुख्या सर्वगुणधिका।
तस्या एव हि देहेऽस्मिन् स्थितिः प्राधान्यतो भवेत्॥ ५॥
यमवाय्विन्द्रदेवानामश्विनोश्च तथा पृथक्।
जज्ञिरे पाण्डवा भूमौ देवकार्यार्थमुत्तमाः॥ ११॥
युधिष्ठिरो यमाज्जज्ञे भीमो वायोः प्रतापवान्।
शक्रादर्जुन एवाभूत् माद्र्यामाश्विनौ सुतौ॥ १२॥
Shyamala, Bharati, Shachi, Usha, and Uma (Parvati)—these five goddesses always resided together within Draupadi. Among them, Bharati Devi is the chief and possesses the highest qualities; she remains the primary governing soul in that body.
The noble Pandavas were born on Earth separately from the deities Yama, Vayu, Indra, and the Ashvins to accomplish a divine mission. Yudhishthira was born from Yama, the powerful Bhima from Vayu, Arjuna from Indra, and the two sons of Madri (Nakula and Sahadeva) from the twin Ashvini Kumaras.
[Garuda Purana, Brahma Khanda, Chapter 17, Verses 4–5 and 11–12]
MAHABHARATA TATPARYA NIRNAYA BY SRIMADHVACHARYA
98-99) Following him, verily Bharati Devi herself came out from the middle of the Yajnavedi. Since he
bears everything Sri Vayu is known as Bharata. Being his wife, she is known as Bharati. Since she is also
the presiding deity of the Vedas, she is known as Saraswati. As she is always under the refuge of Sri
Vayu, who is bliss personified, she is also famous as Sri.
100) She had the Avesha of Shachi, Shyamala and the Usha-devis also. Since these Devis are under the
refuge of Indra, Dharma and the Ashwini-devatas (respectively) they too are known as Sri.
101) She (Draupadi) came to be known as Krishnaa as well. Since she was the best (Utkrushta) amongst
women, since she was of dark hue, since she possessed excellent joy and since she gave joy to whoever
associated with her, she got to be known by that name.
102) As soon as she was born, she was all-knowing. She possessed all ornaments on her and was full of
youth. She never aged and was the most beautiful in all three worlds. She had the special Avesha of
Uma (Parvati) in her. She possessed all auspicious attributes.
[Mahabharata Tatparya Nirnaya, Chapter 18 Bheemarjuna Digvijaya]
SRINARADA PURANA
The Narada Purana echoes this same composition, specifically highlighting the presence of Shachi and Bharati (Sarasvati) inside her:
द्रौपदी च शचीभागाद् भारतीभागसंयुता ।
बभूव रूपिणी साक्षात् सर्वस्त्रीगुणशोभिता ॥ ७२ ॥
Draupadi manifested with the divine portions of both Goddess Shachi and Goddess Bharati. She appeared in physical form on earth, adorned with all the supreme virtues and beauty of a woman.
[Narada Purana Uttarabhaga, Chapter 55, Verse 72]
The Mahabharata Tatparya Nirnaya solves the major issue of calling Draupadi an incarnation of Sri. Sri here doesn’t refer to Lakshmidevi, though she is prominently and mainly known by this word, but in this context it refers to SriBhaaratidevi, the wife SriMukhyaprana Vayudeva.
CONCLUSION
So, in a nutshell, I would like to say that Draupadi was the direct manifestation of Bhaaratidevi, the wife of SriMukhyaprana Vayudeva along with Umadevi, Shyamaladevi, Shachidevi, Ushadevi the wives of Lord Shiva, Yama dharmaraja, Indradeva and Ashvinidevatas. They would follow a system wherein wherein as per the Pandava Draupadi was with, the respective devi would activate and others would be inactive at that time, thus maintaining Panchapatitva.
Hope this helps!
Jay SriRam!
ShriKrishnarpanamastu!