From Bulbapedia, the community-driven Pokémon encyclopedia.
The lake trio is a term used to describe the legendary trio of pixies residing in the three lakes of Sinnoh: Uxie, Mesprit, and Azelf. They are meant to represent knowledge, emotion, and willpower, respectively. They are based off of the Imperial Regalia of Japan: the Mirror of Wisdom, the Jewel of Benevolence, and the Sword of Valor.
Unlike previous trios, all three of the lake trio are of only the Psychic-type. According to legend, when Arceus created the universe it created Uxie, Mesprit, and Azelf, and therefore is believed to be their master.
It is interesting to note that each of the members of the Lake Trio has one of the powers that the God of Christianity, Judaism, and Islam has: Uxie is omniscient, Mesprit is omnipresent, and Azelf is omnipotent. They could also be equated to, respectively, the Greek/Roman deities of Athena/Minerva, Poseidon/Neptune, and Zeus/Jupiter.
The members of the Lake Trio are tied for the lightest legendary Pokémon, and are second for the lightest of all Pokémon (after Gastly and Haunter).
As seen in the pictures below, the two circles in each of the Pokémon's caves are the relative positions of the other two, although the meaning of the shapes of the puddles is unknown.
Mesprit in Verity Cavern.