As most people can guess by the title, the "inner game" of tennis is the game that takes place iin the mind of the player and is played against barriers such as nervousness, self-doubt, etc.
To gain clarity on the mental problems in tennis, the book looks at the concepts of "Self 1" and "Self 2". Self 1 is the name that is given to the conscious ego-mind which likes the tell Self 2, you and your potential, how to hit the ball and play the game. Or, to put it another way, Self 1 is the "teller" and Self 2 the "doer". I found this to be an interesting idea, as we have all caught ourselves talking to ourselves or have seen others talking to themselves during a game. If you ask someone who they are talking to, they will usually say "I'm talking to myself." This, of course, implies that there are 2 "selves", "I" and "myself"- and so is born the idea of Self 1 and Self 2. Pretty astutue observation in my opinion.
Now according to the book, to achieve peak performance, the key is to resolve any lack of harmony between the two selves, as it is the contrary thinking of Self 1 which causes interference with the natural abilities of Self 2. This requires the learning of several inner skills, such as the art of letting go of self-judgements, letting Self 2 do the hitting, recognizing and trusting the natural learning process, and so on- which is what much of the books spends discussing.
I highly recommend this book for anyone who plays tennis (or any other sport for that matter) as it does a great job in dealing with the fact that many of our difficulties in tennis are indeed mental in origin. Other helpful books for tennis players I've come across include Treat Your Own Tennis Elbow
and Treat Your Own Rotator Cuff