Watching the movie Next starring Nicholas Cage. Have decided prescience is memory theft. We see an exchange between people happen, come to a conclusion, then the film jerks time back to show it has not happened yet and our protagonist takes a different path so what we saw never happens. So, he's stealing memories from the people around him, he remembers what no longer will happen and they don't get to.
Clearly the theft of future memories is what powers his abilities. There is no other logical conclusion.