Reroll
A reroll is an extra chance to roll against a check. Multiple rerolls can stack, after which the best of all rolls is taken. In the case of negative rerolls, the worst of all rolls will be taken.
For instance: Let's say Locke has two abilities active that each grant him a sneak reroll. When he hides and sneaks into an occupied room, he'll then have 2 additional attempts to pass the sneak check and remain undetected, instead of just the single roll attempt. So let's say he rolled a 30, an 80, and a 5. His final roll would be 80, as it was the highest of all rolls.
A partial reroll imparts a chance for an additional reroll. For example: A reroll displayed as 2.3x would have a 30% chance of an additional reroll, for a potential total of 3 rerolls. The other 70% of the time, it would only be worth 2 rerolls.