I hate it when they use that word. People think it means all sorts of things it doesn't mean. What they mean when they say "toxins" is the waste product of metabolism, which is left over after the process of initiating muscle contraction. People call this a "toxin" simply because it's a substance that your body can't use and will eliminate, not because it's deadly or anything. This is what makes your muscles feel sore, stiff, achy, etc., especially after a particularly strenuous workout or stressful situation. Your circulatory carries this away in time, but massage speeds up the process of flushing the waste products out of your muscles and into your bloodstream with all the kneading and pushing being done.
That's what they're talking about. They just did a superbly bad job of communicating clearly.