These puzzles are positions from real games where one player had the chance to win if they found the right move(s). In each one your task is to find those moves. You won't play the whole game, just long enough to convince the computer you found the winning combination. They are intended to be bite sized fun and practice.
Be careful, at every step one move is clearly better (according to KingsRow) than every other and should win material or the game. Other winning moves are possible and may or may not give you a second chance but most moves will draw or lose. Your job is to play the most accurate winning line.
The settings page has options for difficutly, piece set, whether you play from the top or bottom, sound levels, etc. Check the user guide for more detailed instructions, or the forum for other questions.