The quotes relate directly to his philosophy that your life is your thoughts, and to change your life you must change your thoughts. I remember the day in my early 20's when this concept occurred to me, and I love the way Tolle explains it, below in its purest form:
The primary cause of unhappiness is never the situation but your thoughts about it. Be aware of the thoughts you are thinking. Separate them from the situation, which is always neutral, which always is as it is. There is the situation or the fact, and here are my thoughts about it. Instead of making up stories, stay with the facts. For example, "I am ruined" is a story. It limits you and prevents you from taking effective action. "I have 50 cents left in my bank account" is a fact. Facing facts is always empowering.
Why do anxiety, stress, or negativity arise? Because you turned away from the present moment. And why did you do that? You thought something else was more important. One small error, one misperception, creates a world of suffering.
People believe themselves to be dependent on what happens for their happiness. They don't realize that what happens is the most unstable thing in the universe. It changes constantly. They look upon the present moment as either marred by something that has happened and shouldn't have or as deficient because of something that has not happened but should have. And so they miss the deeper perfection that is inherent in life itself, a perfection that lies beyond what is happening or not happening. Accept the present moment and find the perfection that is untouched by time.
What a perfect way to tell us to live in the moment! Not to worry about tomorrow or yesterday but to think about the moment of now. It doesn't mean not to prepare for tomorrow -- but don't LIVE in it. It also means not to live in yesterday, rethinking the things we did and making them seem better or worse in our minds. Just live the moments and remember everyone else is doing the same thing, doing the best they can with what they know (and that includes our parents).