Perhaps we should have started with the King? The King is the most important piece in chess. If it gets checkmated then the game is lost. If the opponent's King is check mated then victory is in your hands. The king can go 1 square in any direction. Two kings cannot stand next to each other and this is actually why king and rook can checkmate a king. From its initial position at e1 or e8, it can also make a move called castling. This can only be done if the king has not moved a single time and if the king will not pass a check or end up in check while castling. The king can castle kingside by moving e1-g1 and having rook jumping h1-f1. And it can castle queenside by moving e1-c1 and having rook jumping a1-d1. Castling is a very important move because it is a way of protecting the king and also bringing the rooks into play.
In the opening and the middlegame, the king is a weak piece because it mostly causes problems and you have to think about its safety all the time. As more and more pieces are exchanged off the board, the king increases in strength. With a few pieces exchanged, including the queens, the king can already start planning a journey into the center of the board. In the endgame, the king is strong in many ways. It can support passed pawns into promotion. It can stop the opponent's passed pawns. It can eat pawns, especially those that are blocked by the own pawns or pieces. It can win enemy pieces, the famous example is Nd4 and Bd5 can be forked by a king on c5 or e5.
The king wants to be in the center of the board for several reasons. From there, it threatens to quickly attack one of the two flanks. It runs a smaller risk of getting mated. It supports the other pieces and pawns that want to become established in the center. It limits the opponent's space. It increases the chance of mating the opponent's king.