The "DC" in DC generator is short for direct current. For a generator to be classified as a direct current generator, it must meet two criteria. Firstly, the current provided by the generator has to be conducted by a loop of specialized wire on the inside of the generator that constantly rotates. Secondly, the electrical current generated by the loop of wire must move in only one direction as opposed to two. These criteria are met and managed by a piece of equipment called the commutator.
Inside a DC generator, the commutator is split into two segments. Both of these segments are insulated so no electricity is actually transmitted directly from one part of the commutator to the other. The loop of wire that rotates is connected to both ends of the commutator at each end. There are also two brushes made of carbon connected to the commutator. These carbon brushes each have a very specific purpose--one brush is responsible for pushing the electrical current out of the generator to whatever devices are being powered, and the other brush pulls electrical current into the generator.
All of the components on the inside of a DC generator are synced up to operate at very specific time intervals. Once the electrical current gets going inside of the generator, the segment of the commutator that holds all the electricity that will be going outside of the current is always touching the carbon brush that pushes the charge outside of the the unit. The electricity is essentially "swept" from the commutator to the electrical devices connected to the generator by the brush.
Large DC generators will have many commutators inside them as opposed to the just one that small versions will have. Because of this, these large generators also have many different segments of wire loops and are essentially performing the same job as a small generator multiple times simultaneously. This ultimately can provide much more electricity for much longer periods of time.