This piece of granite is, I believe, a relic from the Newtowne Market. It appears as though it was at one time part of the pediment. There are, however, steps carved out of the backside.

People sit here in ones and twos to drink coffee or chat. Kids like to climb on it and harass the pigeons. Its form is such that several people or groups can find their own personal space at once and often there are a number of different "groups" sharing this slab of granite sitting on different edges.