It's some sort of sentient life form, but its exact nature is never made clear.
When they first encounter the transformed Andy and Tariq, the Doctor says he doesn't know what is possessing them:
DOCTOR: Human beings are sixty percent water, which makes them the perfect host.
ADELAIDE: What for?
DOCTOR: I don't know.
Later on, we discover that the whatever-it-is possessing them is intelligent enough to seek out new hosts, infiltrate the base, compromise the rocket, and understand Ancient North Martian:
ADELAIDE: Maggie, can you hear me? Do you know who I am? Your commanding officer, Captain Adelaide Brooke. Can you tell me what happened?
DOCTOR: Hoorghwall in schtochman ahn warrellinsh och fortabellan iin hoorgwahn.
ED: What language is that?
DOCTOR: Ancient North Martian.
ADELAIDE: Don't be ridiculous.
ED: It's like she recognised it.
The Doctor speculates that it was known by the Ice Warriors of old and they were the ones who trapped it under the ice on Mars:
DOCTOR: They tell legends of Mars from long ago, of a fine and noble race who built an empire out of snow. The Ice Warriors.
ADELAIDE: I haven't got time for stories.
DOCTOR: Perhaps they found something down there. Used their might and their wisdom to freeze it.
Perhaps the best hint we get to its nature is when we actually hear it speaking, in English, using Maggie as a mouthpiece:
MAGGIE: Earth is so much water.
YURI: Yeah. Just look at her. Forty million miles away.
MAGGIE: It has so much beauty.
(Her voice changes, as if she is many in one.)
MAGGIE: We should like that world.
(Yuri turns around and sees Maggie, water pouring out her mouth.)
That's pretty much all we know about the entity dubbed The Flood: it's evil, intelligent enough to destroy Bowie Base One and plan invasion of Earth, and feared even by the Ice Warriors.
Interestingly, rumour has it
that the Flood may be making a comeback in Series 10, so we may find out more about it quite soon! I'll be back to update this answer if so.