The type of Vaishnavism that was practiced/popularised in Western Bengal (Gauda Desh, c.f. Bangla Desh, Eastern Bengal). Gaudiya Vaishnavism is the teachings of Sri Caitanya, whom we follow as the recent Incarnation of Sri Krishna, whose appearance and pastimes are referred to in the Bhagavatam long in advance of the appearance of the Lord (which was 500 years ago in Gauda Desh, hence the name now of "Gaudiya Vaisnavism", or "that Vaisnava style which Sri Caitanya of Bengal re-established or re-enlivened at least".
Although a revivication of the bhakti tradition, two major differences between Gaudiya Vaishnavism and the other Vaishnava sampradyas are: (1) that instead of envisaging a plethora of different Gods and Goddesses, Krishna (Vishnu) is worshipped as the supreme manifestation (avatara) and source (avatari) of Godhead; and (2) that all people, regardless of caste (varna) or station in life (ashrama), could be self-realised through their activites performed in loving service and devotion to Krishna. In recent times Bhaktisiddhanta Sarasvati Thakura and Srila Bhaktivedanta Swami Prabhupada took the latter point as far as allowing non-brahmanas to serve the Deity, including non-Indians.
See also: Vaishnavism.