Vipassanā in the Buddhist tradition means insight into the true nature of reality, namely as the Three marks of existence: impermanence, suffering or unsatisfactoriness, and the realisation of non-self. Vipassanā-meditation is an ancient practice taught by Buddhas, reintroduced by Ledi Sayadaw and Mogok Sayadaw and popularized by Mahasi Sayadaw, S. N. Goenka and the Vipassana movement, in which mindfulness of breathing and of thoughts, feelings and actions are being used to gain insight in the true nature of reality. Due to the popularity of Vipassanā-meditation, the mindfulness of breathing has gained further popularity in the west as mindfulness.
I would like to refer anyone interested in learning more about mindful meditation practices to Mindfulness In Plain English by Ven. Henepola Gunaratana.