These chaps guard the entrance to shrines. One has an open mouth, the other a closed. The open mouth represents ‘a’ – the beginning of the Sanskrit alphabet (syllabary?) the closed mouth represents ‘un’ – the end of the same. This symbolizes the beginning and the end of all things. If you put them together, you get ‘aum’ which is a holy sound in some religions.

(I had to double check Wikipedia because I can never remember which of the statues is which. There’s lots of other interesting factoids other there. )