The statue was 'acquired' by the crew of the HMS Topaze, under the command of Richard Ashmore Powell, who visited Easter Island in 1868. The Islanders and the crew moved the statue, which had been in a stone house at the ritual centre of Orongo, and is estimated to weigh around four tons. It was taken to the beach and floated out to the HMS Topaze on a raft.
The Moai is named Hoa Hakananai'a, which is its original name, and is thought to mean 'stolen or hidden friend'. There is also another, smaller statue, known as Moai Hava, which is also in the collections of the British Museum. It was originally painted red and white, but the pigment washed off in the sea.
Hoa Hakananai'a is on display in Room 24 of the British Museum, accessible on the opposite side of the Great Court from the main entrance. It is free to visit Room 24. For more, see http://www.britishmuseum.org/explore/highlights/highlight_objects/aoa/h/hoa_hakananaia.aspx