Wesley actually they play on their own, you just predict the next move of the opponent and you make your moves too. if your opponent don't move in the way you have predicted then you are called to play as usual.
Now I'll try to explain to you how you give your conditional moves.
when you play on the right of your chessboard there are 4 options Analyze, Settings, Offer draw and resign.
But when you have made your move if you go back to the board appears a fifth option Conditional moves, if you click on that and then click on add a new line it opens a window and you can make the move of your opponent and then your move again and so on, you make one scenario, if you don't like it at the end or you want to change it, you delete and do it again. You can make different scenarios everytime by clicking on Add a new line
this helps you a lot with players who play very slow or it gives you also the ability to study your next moves and see the outcome of different scenarios you have given, so if you don't like the outcome you delete that scenario and you plan something else.
I have come across messages during matches against other players - on Chess.com - a couple of times now in Chess Online. That my move has prompted a conditional move from my opponent. I'd like to know more about such moves. What moves are considered conditional and how are they triggered?
I personally feel they give the opponent an advantage since they may not have made that particular move if they'd played on their on.