Edge pieces can anchor flips that influence moves to all regions of the tablier. If played poorly, this can poison later moves by causing players to flip too many pieces and open up many moves for the opponent. However, playing on edges where an opponent cannot easily respond drastically reduces possible moves for that opponent.
The square immediately diagonally adjacent to the corner, when played in the early or middle game, typically guarantees the loss of that corner. Nevertheless, such a corner sacrifice is sometimes played for some strategic purpose (like retaining mobility).
Playing to the edge squares adjacent to the corner (called the C-squares) is a little less dangerous but can give the opponent powerful forcing moves.