The board of Ultimate Tic Tac Toe is made up from 9 ordinary Tic Tac Toe boards, hence there are 81 possible fields. Each small Tic Tac Toe board will be called a local board and the big Tic Tac Toe board will be called the global board. A player can start anywhere he'd like to on a local board. According to the location he played on a local board, his opponent will be sent to that position in the global board. The opponent can now play on the local board, keeping in mind that he will send the other player to the relative position on the global board.
A victory of a local board is the equivalent to a marked tile on the global board. To win the game, one has to win 3 horizontally, vertically or diagonal aligned tiles of the global board.
If a local board is won or draw, no more moves are allowed there. In case a player was sent to such a board, he is allowed to make his next turn on every other local board. It's possible that the game ends in a draw, because no more legal moves are allowed.
Don't you understand the rules yet? Here you will find the rules explained in more detail.