what is the "double switch"?

You are making a strategic change, perhaps a pinch hitter for the pitcher who may or may not stay in the lineup.

You also make a defensive change with the last batter of your offensive inning, placing the new pitcher in that last spot so he will not bat for nine batters, allowing you flexibility with your pitcher.

Note that a double switch may also apply to other weak hitting players - e.g. defensive specialist (all glove no hit). Essentially you are making two changes at once and flip flopping the players in the batting order in order to postpone the agony of watching that player try to swing the bat.

Note that this also applies primarily in leagues where they play real baseball - no DH.