The Chakravyuha( or Padmavyuha) looked something like the one in the figure above. The basic concept of the Chakravyuha, was that it would be a multi tier formation, arranged in the form of concentric rings, each tier consisting of soldiers. While the infantry would be forming the outer tiers, the most experienced, skilled warriors would be at the inner tiers. Now imagine this formation attacking the enemy, what would effectively happen, is the moving circles enclose the warriors, creating a sort of wall around him, leaving no route out. If you take a footballing analogy, it is akin to marking the best player of the opposite team, and restricting him from scoring the goals.
The Chakravyuha was designed by Drona, as an attempt to capture Yudhistir alive and defeat the Pandavas again. Now only 4 people on the Pandavas side, knew how to penetrate the Chakravyuha and break it- Arjun, Krishna, Pradyumna and Abhimanyu. Of these 4 Pradyumna choose not to fight at Kurukshetra, and Abhimanyu knew how to enter it, but not exit it. That left only Krishna and Arjun, the Kauravas took care of that, by mounting an attack on the Virat kingdom, by the Trigartas. What this meant was both Arjun and Krishna had to be away from the battlefield, and the Pandavas were rendered vulnerable now.
The only other option left was Abhimanyu now, who told them that while he knew how to enter the Chakravyuha, he did not know how to exit. The toughest part in breaking the Chakravyuha was this, assuming you break one tier of defense, and enter the next tier, the former tier immediately regroups again. Now unless you know how to get your way back, you are effectively trapped inside. Yudhistir assured Abhimanyu that they would follow him, once he breaks inside, and would mount an assault.
Enter Jayadratha, the brother in law of Kauravas, married to their sister Dussala. Apparently during the Vanvaas time, Jayadratha, had carried away Draupadi forcibly, wanting to make her his queen. However Arjun and Bhim caught up with him, and defeated him. They were about to kill him, when Yudhistir, intervened saying that would make their sister Dussala, a widow. Jayadratha's life was spared, but he was humiliated, by shaving his head, leaving only a patch of hair. He swore revenge on the Pandavas for this, and prayed to Lord Shiva, asking for a boon, by which he could defeat them. Shiva, said that it was impossible to defeat the Pandavas, especially Arjun. He however granted him a boon, saying that for one day however he could keep the Pandavas at bay, that too excluding Arjun.
When Abhimanyu broke through the first layer of the Chakravyuha, and entered inside, the Pandavas sans Arjun followed suit. However that layer once again regrouped, and this time it was Jayadratha guarding it. Taking advantage of the boon offered to him, Jayadratha, kept Yudhistir, Bheem, Nakul, Sahadev at bay. What this meant was as Abhimanyu entered deeper into the Chakravyuha, he was all alone, as layer after layer behind him closed off. The Pandavas could not follow Abhimanyu inside, as Jayadratha held them off, in a fiercely contested fight.
Abhimanyu did not enter the Chakravyuha alone, he knew the dangers of it. What he expected was that he would lead the way, and the rest of the Pandavas would be following and guarding him. Alas with Jayadratha proving to be the obstacle, he was forced to fight a lonely battle against the Maharathis of the Kaurava army, resulting in his death.
Also it was not possible for a flying wedge formation to break the Chakravyuha, for the reason, it was divided into layers of concentric circles. So every time a layer broke, it would immediately regroup again, in effect it was both a defensive and offensive formation.