Titans are a new type of ship in Sins of a Solar Empire: Rebellion. Titans are very large and powerful ships able to support fleets or take command of the battlefield; they are presumably on a similar scale to the Super Star Destroyers of the Star Wars saga, or at least that's what the developers compare them to.
Titans are, for the most part, unstoppable except by another Titan (assuming that your titan is at an equal level) or an insanely large fleet. Their primary role is equivalent to a bunker buster bomb: an unstoppable steamroller. Even a lower level titan is capable of decimating massive fleets by itself and when fully upgraded, becomes the most feared object in the game.
Titans are built in a structure so large that it dwarfs even a starbase. For example, the TEC Titan Foundry is an enormous shipyard that casts a looming shadow over half the gravity well. Titans must be researched and built in four stages, each of which alerts other players of what you're up to so they'll have a chance to catch you while you're vulnerable (having funneled lots of resources into your Titan project).
A player or AI can only have one Titan at a time; it also occupies 2 Capital Ship Crews and 150 Fleet Supply - not that much, compared to resource costs and the sheer size of the ship.
Upon a Titan's death, the next Titan built will retain the levels gained by the previous one.