What Sartre means by this is that we have absolute responsibility for our own lives, that we must live with the consequences of our free choices, and that if we are not prepared to do so then we can always commit suicide—otherwise we deserve everything we get.
Sartre precedes these remarks in Existentialism and Human Emotions by stating that there are no accidents in life. He uses the metaphor of war to drive home this point. Like war, life isn't something that comes to him from the outside; on the contrary, it is his; he owns it. Therefore, he is his own life insofar as he has chosen to live it.
He may not have started the war, just as he wasn't responsible for bringing himself into existence. But now that he does exist, now that he's part of the never-ending war that is life, he has a choice whether or not he wishes to continue with it.
If he does, then he must accept the consequences, and everything that happens to him is richly deserved. If he doesn't, then there is always the option of suicide, which will remove him from the field of battle, so to speak. Stretching the military metaphor a little further, one could interpret Sartre as saying that death through suicide is akin to desertion in war.
However constrained we might think we are in making decisions, there is always a choice to be made, and in Sartre's grim, uncompromising variant of existentialism, exercising that choice often ends in death.