You can launch play game mode from the play game toolbar icon or the Play->New game... menu item.
In play game mode you play a game against the computer. In this mode the access to many features which are not applicable to this mode are prevented. Instead you have access to operations specific to game play e.g. Resign, Offer draw etc, etc. While playing the game you can access the features via the menus or the play icons which allow you control over the game, moves and assistance.
During play mode if you have Guess move enabled you will have assistance in finding the best move. The quality of moves are highlighted using colour coded square highlights. These can be a great learning aid and help the playing realise earlier when a move is perhaps not as good as initially thought. Of course this can be turned off in the Preferences->Board tab. Here is an example of the coaching move highlights:
In addition the coach, if enabled, will watch your play and if it sees you make a mistake or miss a puzzle like strong move then it will alert you to this with a coach warning dialog and give you the opportunity to take back your move or discover the refutation.