Roller bridges are saddles some mainly used to upgrade TOM bridges and vibratos on guitars to get rid of the frictions on the sharp bridge points to decrease tuning instability and string breakage. Most think that there'll be no tonal difference between a traditional Tune-O-Matic saddle and a roller saddle.
Why Roller Bridge
TOM bridges have a rather thin edge upon which the string rides. With an appropriate break angle, this arrangement is great for sustain, but if the edges are a bit sharp it can lead to string breakage, especially if you do a lot of bending.
Rollers eliminate that issue. The advantages of rollers are obvious: the contact is round and the rollers turn as you're tuning strings to the pitch. You're still bending strings and a roller bridge would make the return to pitch more accurate than a standard tune-o-matic bridge.
What's More
However, bridge friction is only one of several things that can cause tuning instability. And some roller bridges will be loose and affect the stability. So putting in a roller bridge won't magically solve all your tuning instability problems if you've also got a sticky nut, bad string trees, tuning machines, new strings that are still stretching, etc. To achieve the best sustain and stability, I recommend that you also change the guitar nut and lubricate the slots in the nut just before each performance. If you want to go one step further you can also add locking machines, and most bases will be covered.