As a piece moves, it leaves a trail of all the places it has been. This is its Timeline. Its timeline is represented by arrows. Since your pieces are time-traveling entities, you can capture a piece either by landing on the piece or by landing on its timeline. When you land on a piece's timeline, its timeline from that point on is erased, and pieces it has captured come back. Its like going back in time and killing Napoleon in year 1800. Any individuals Napoleon killed after 1800 would come back to life.
 
A few restrictions. A piece cannot land on its own timeline, nor on the timeline of a friendly piece. This would be like going back in time and meeting yourself - strictly forbidden. This means that your timelines create barriers. Also, you cannot enter an enemy square that contains a dead friend. Dead pieces are indicated by a toppled icon. Technically, a piece is never dead, because it can be brought back to life when its captor is captured.
 
If a piece is more than 8 squares away from the square of capture, it is safe from the effects of time.
 
Have fun.