"Mindfulness practice offers the restraint necessary to overcome the tug of desire upon the senses. As we notice the mind wandering off to explore a gratifying train of thought, or as we notice the body's urging to nudge ourselves into a more comfortable position, we gently abandon the impulse and return attention to the primary object of awareness. We do this again and again, until the mind becomes content with being fully present [with] what is manifesting here and now in the field of experience, rather than rushing off for some other form of stimulation. As the mind settles down it becomes considerably more powerful, and thus more empowered."
Please notice, "we gently abandon the impulse." Thoughts and sense desires will arise. But we don't try to get rid of them. We notice what is happening. In doing so there is clear seeing of what is arising, of what is present here and now.
"In this mode [mindfulness] the mind is said to be unlimited, and is capable of experiencing freedom through wisdom. Its freedom comes not from the license to broadly explore a shallow terrain, defined by its likes and dislikes, but rather from the ability to shake off the contraints of desire altogether and plunge deeply into investigating the field of experience as it is. It turns out that what one sees, hears, smells, tastes, touches, or thinks, is not as important as how one does this."
The quotations above are taken from an article by Andy Olendzki published in Tricycle (Summer 2007). The article is a commentary on The Parable of the Six Creatures S 35:247