There's enough of it set up that you get the idea. You see that there is a senate, with senators in pods that presumably vote of things, and that a supreme chancellor is the top authority in said body. You know that Padme is a senator and opposes the war with other government officials. You know that a seperatist movement within the republic created the clone wars. You know Anakin and Padme fell in love and are secretly married. You know that Dooku is a sith working with a higher mastermind named Darth Sidious. You know that Anakin was seperated from his mother and the he had dreams of her before she died and that he killed the sandpeople--these last points would have been made clearer and emphasized had the film been actually designed as a stand-alone piece. But for one that is supposed to fit into a trilogy it is incredibly self-sufficient.

Additionally, all that other stuff gleaned from the first two films is boring, superficial expository information. How does the voting process in the senate particularly work? Who cares. How did Palpatine actually get himself voted in? Who cares. How did the clones specifically get created? Not necessary. How did the Republic stand at the height of its glorious power? Who knows--TPM and AOTC don't show it either, as Lucas has stated many times we enter TPM with the Republic already crumbling and corrupted. Furthermore, all the actual character exposition that we aren't privy to--such as Anakin's courtship and his relationship with his mom and Obi Wan--are so poorly handled that the best thing about ROTS is that it ignores such things and simply presents them as they should be, with motivation, believable writing and dramatic interest.
We don't need to learn EVERY detail. This is what made the original film so intriguing. In fact there is a specific literary device to describe this technique--"in media res". In the middle of things. The story begins in the thick of action and increases audience interest by not revealing how things exactly got to be where they are. ROTS accomplishes this nicely--it explains things and shows how the important events occured but enough is left unsaid that it not only makes things more interesting but the audience fills it in with their imagination much better than the shitty writing Lucas used to give us those same things in AOTC.