The moon creature is a giant living creature which had been developping inside its egg, Earth's moon, for possibly as long as 4 billions of years. It hatched in 2049 after an intense one year growth period during which it increased its mass dramatically, breaking the Moon's crust in the process.
At birth, it weighted 1,3 billions tons, most of it being the egg it itself was ready to lay as soon as it was being born, and which was to become Earth's new moon, along with the dust left by the disintegration of the former moon's crust.
The creature itself is composed of a short somewhat moth-like body with long flayed tail and of two pairs of diaphan wings that composed most of its mass. After laying its egg, it flew away toward deep space.
Its whereabouts afterward remain unknown, as do its origins: was the egg initially layed by another creature or did it evolve on spot, possibly as a result of the planetoid Theia with the Earth. This also raises the question of a possible panspermia originating from Theia. But this hypothesis is highly speculative.
Source: Doctor Who universe, 2014, Kill the Moon, written by Peter Harness.
Here are two 3D echography of the Moon dating hours prior to its hatching.