In a dc generator, current is forced to flow in one direction; in an a/c generator is it allowed to flow in two. A/C power is widely used because it can be transmitted much more economically via step up power transformers...reducing current flow and reducing transmission wire size and power losses...
Remove the rectifiers (diodes) which prevent reverse current flow in a typical generator and you change a dc to an ac generator...
See here for a more complete discussion and diagram:
http://en.wikipedia.org/wiki/Alternator#Principle_of_operation
generators and alternators are slightly different...see the bottom of the WIKI page for further information.
There are different types of generators, see commutators to understand how current flow direction may be governed:
http://en.wikipedia.org/wiki/Commutator_(electric )