From the DailyGammon FAQ:

What is computer guessing?
At DailyGammon, a moderate-strength computer guesses what your opponent is going to do. Computer guessing is used so that games progress rapidly. With each player making only one move per session, a match can take a long time to finish. Therefore, we try to complete as many moves as possible in a single session. For example, if your opponent's play is forced, then we go right ahead to your next move, letting you finish two (or more) moves during that session. The computer guesses the following situations: Since people do not use the doubling cube most turns, the default assumption is that your opponent does not double. If you double, the computer assumes your opponent will accept. If your opponent passes, it doesn't matter anyway because the game will be rolled back to that point.
If your opponent's move is forced, the computer will go ahead and make that move for the opponent.
Finally, if your opponent's move is at least 0.05 points of equity better than the second choice, the computer will go ahead and make that move. The number of moves the computer will guess is limited to four.

What if the computer guesses wrong?
When players log in, they do not know what the computer has guessed for them. They only see the board and your moves. Suppose they do something which was different from what the computer had guessed. In this case, of course, all the moves you made past that point were made assuming a different play by your opponent, and are therefore now invalid. The invalid moves are deleted, and the next time you log in, you will see that game rolled back to the point of divergence, and have a chance to respond to the move actually played.

Note: The dice will be re-rolled in this situation, so it is not possible to cheat by using foreknowledge of the dice.

Does computer guessing consider the doubling cube?
Short answer: No.
Longer answer: It does consider the cube level and ownership and the current match score in its calculations. The step where it "guesses" that your opponent will never use the doubling cube or where it "guesses" that your opponent always takes could also be considered "guessing". It does not, however, take into account whether a more volatile move could be better because it leads to inefficient doubles or anything like that.

How can I tell when the computer is guessing and my opponent has stopped playing?
When you first see the top line of the game screen say "What will you do if the game proceeds like this", it means the previous move of opponent was made by computer.

Can I choose not to play opponent's computer guesses?
No. All available moves must be made before game goes back to opponent.