new game

The "+" symbol means you threaten his king and also means he is forced to deal with that threat as king "suicide" is forbidden in chess.The king never leaves the board.
Every time your move thraetens your opponent's king it will have a "+" symbol at the end.The same when a move of your opponent threatens your king.
The "x" symbol means your piece or pawn took and enemy piece or pawn.
So Bxf2+ means :Bishop takes("x" symbol) at f2 and threatens the king("+" symbol).