Essentially, yes.
The nuclear fission produces enormous amounts of heat and you use the heat to produce steam to drive a steam turbine which in turn drives the alternator.
It’s basically a conventional coal powered plant on steroids. A conventional coal powered plant uses coal to heat the water instead of nuclear fission.
Apart from photovoltaics, electricity is generated by driving the alternator ( electric generator) using a mechanical device such as a steam turbine, hydraulic turbine, gas turbines, diesel engines or IC engines or just about any device that will output mechanical energy.
A steam turbine converts thermal energy from high pressure and high temperature steam into mechanical energy which is outputted at the shaft of the turbine which in turn drives an alternator ( short for alternating current generator ) that produces electricity.
Similarly a hydraulic turbine converts hydraulic energy into mechanical energy that drives the alternator.
The difference between a coal powered plant and nuclear plant is how the water is heated and made into steam to drive the steam turbine. A nuclear plant uses nuclear fission which can generate enormous heat and that is used to generate the steam that drives the steam turbine. The only difference is the source of the heat for the steam.
And for people commenting that Beta Voltaics, Magneto Hydrodynamics, Fuel cells, batteries etc can produce electricity without a mechanical prime mover with the exception of photovoltaics, can any of them power an electric grid or produce enough power to do so? This specific answer pertains to power generation for an electric grid and other than photovoltaics, most others are incompabale of generating power to supply a grid and batteries are for low power devices ( cars with Li-Ion or NiMH batteries have to recharge through the electric grid mostly powered by conventional electric power generation and some from photovoltaics.