trāyastriṃśa (Sanskrit; Pāli, tāvatiṃsa). A heavenly realm located, according to traditional cosmology, on top of Mt. Meru above the realm of the four great kings (caturmahārāja; lokapāla) who guard the cardinal points. Śakra (Pāli, Sakka) is the king of both these worlds. Occasionally sages visit this realm and according to tradition the Buddha spent some months there teaching the Abhidharma to his mother when she was reborn in this heavenly realm. Mahāmaudgalyāyana was also a frequent visitor. The name ‘thirty-three’ derives from the fact that this world is the residence of the 33 gods of Hinduism, an ancient mythological notion originating in vedic times.

A Dictionary of Buddhism, Oxford University Press, 2003, 2004 (which is available in electronic version from answer.com)

三十三天  The thirty-three gods (trāyastriṃśa) who live on the top of Mt. Sumeru in the second of the six heavens of the desire realm 六欲天. Śakra　帝釋天 dwells in the center with eight other gods in each of the four directions. Also rendered with the hybrid transcription/translation as 忉利天.