Trap a line of your opponent's discs between two of yours and they all flip to your colour. Most discs at the end wins.
A minute to learn and a long time to play well, against a computer that plays the corners properly.
You play black and move first. A legal move has to trap at least one line of white discs between the disc you place and another of yours.
Every trapped disc flips, in every direction at once, so a single move can turn a whole corner of the board.
If you have no legal move you pass, and the game ends when neither side can move, usually when the board is full.
Count at the end rather than during. The score in the middle of a game means very little, because almost everything can still flip.
A disc in a corner can never be flipped, because there is no square on the other side of it. Corners anchor whole edges, which is why good players give up discs to get them.
Usually the opposite. Having few discs in the middle game means your opponent has fewer safe moves, which is how you end up taking the corners.
You pass and your opponent plays again. If neither side can move, the game is over and the discs are counted.
Same game, different name. Othello is the trademarked version with a fixed starting position, which is what is used here.
Reversi was invented in the 1880s and rediscovered as Othello almost a century later, with a marketing line about a minute to learn and a lifetime to master that happens to be true.
The counterintuitive part is that taking lots of discs early is bad. Mobility matters more than material, and a player with two legal moves is usually about to lose a corner.
The computer here weighs corners and edges heavily, so the higher levels will punish a greedy opening.