Bubble Fun is a turn-based game. The point of the game is to create long chain reactions of popping bubbles, and take over the board with your color.
Every time you click on one of your bubbles (purple) the number goes up by one. Once you reach the number 4, the bubble will burst and "infect" the neighboring 4 bubbles. The value of the neighboring bubbles goes up by one when that happens.
Bubbles on the edge of the board only have 3 neighbors, so they are ready to pop at the number 3, not 4. Bubbles in the corner only have 2 neighbors, so they pop after the number 2.
Ultimately you're supposed to "infect" all bubbles on the board with your color. That can be done fairly quickly, but if you end the game too quickly, you won't get a very high score.
To get a high score, you need to create really long chain reactions and keep the game going for as long as possible, without either you or your computer opponent winning the entire field.
The longer you keep the game going, the more volatile the board becomes. The computer may be down to just 1 or 2 bubbles, but if "all the bases are loaded" he may regain the entire board with one long chain reaction... so the longer the game goes, the riskier it becomes and you might lose all your points. You only get the points if you actually win the game and change the entire board to your color.
PS: Sorry, the "save highscore" feature at the end of the game is currently disabled because I'm migrating my game site PCpuzzles.com to a new server.)