Strike simply means to deal damage equal to the unit's power. For example, if a strikes, it strikes for 3 damage.
In a fight, units strike each other simultaneously. Some abilities allow units to strike first, e.g. Lance.
Split power units deal damage equal to their attack power when they strike.
Sometimes the striking unit and the unit being struck are at different locations, and some effects (e.g. ) care about the location of the strike. For clarity, the strike occurs at the location of the unit being struck.