Stones: One player plays black and the other plays white. Each player takes turns by placing one stone on an intersection on the board. Black goes first and if it is a handicap game (see rank) white goes first. Once a stone is placed, it stays there throughout the game unless captured. Each turn a new stone is placed.
Liberties: To stay on the board, a stone needs at least one liberty. A liberty is an empty intersection adjacent to the stone. One stone with no other stones right next to it has 4 liberties. If all liberties are taken by the opponent, the stone is captured and taken off the board by the opponent.
Groups: When stones of the same color are adjacent to each other (or on each other’s liberties), they become one group and share liberties. So if 1 stone is next to another stone of the same color, instead of 4 liberties, the 2 of them now have 6 liberties.
Capture: If a stone or a group has only 1 liberty, it is said to be in atari, which means the stone or group can be captured on the next move if you don’t respond. Typically, depending on the situation you may want to protect against such capture. There are other moves such as the ladder and net that ensure capture without directly capturing.
Cut: Since stones are not connected diagonally, they can be cut off from one another. Entire groups can be disconnected and put in danger with a proper cut.
Ko: Rule of Ko is the rule that board positions cannot be repeated. If your stone is captured in such a way that a stone can be captured right back but leads to the previous board position, you cannot capture it back without first playing elsewhere and forcing your opponent to respond (this is called a ko threat).