How mindfulness meditation is different from other concentration-based meditation (e.g., transcendental meditation)

One way of understanding mindfulness meditation is to compare with concentration-based approach.

Mindfulness should be practiced with an attitude of nonjudgmental acceptance. That is, phenomena that enter the individual's awareness during mindfulness practice, such as perception, cognitions, emotions, or sensations, are served carefully but are not evaluated as good or bad, true or false, healthy or sick, or important or trivial. Thus, mindfulness is the nonjudgmental observation of the ongoing stream of internal and external stimuli as they are.

Concentration-based approaches train participants to restrict the focus of attention to a single stimulus, such as a word (e.g., a mantra), sound, object, or sensation. When attention wanders, it is redirected to the object of meditation. No attention is paid to the nature of the disraction. Mindfulness meditation, in contrast, involves observation of constantly changing internal and external stimuli as they arise.

Baer, R.A. (2003). Mindfulness training as a clinical intervention: A conceptual and empirical review. Clinical Pschology: Science and Practice, 10, 125-143.