Quick explaination:
When approaching a corner, one does not just walk around it, or poke one's head around it. One steps back a ways, so as to be 'going wide' around the corner, and proceeds very slowly, inching around and looking for target indicators (body parts, weapons, shadows, smells, sounds) in the region to be entered. It is called slicing the pie (I think) because if you treat the corner as the fixed point at the center of a circle and you treat your path around the corner as a trip around a circle's circumference, your action is proceeding forward is like taking a slice out of a pie.
Clear as mud?
Mike