This is a thornier subject than one might think. The statue commonly known as Eros was created by Sir Alfred Gilbert in 1892-1893 as part of a fountain built in honour of the 7th Earl of Shaftesbury, a philanthropic politician after whom Shaftesbury Avenue was named. 'Eros' is one of the most famous landmarks in London; the Evening Standard newspaper incorporates its image in its masthead.
However, the statue does not depict Eros, the Greek God of love. The statue's real name is sometimes thought to be the 'Angel of Christian Charity' but this is also wrong. The statue was originally titled 'Anteros Agape', and it depicts Eros's tamer twin, Anteros, the embodiment of "reflective and mature love, as opposed to Eros or Cupid, the frivolous tyrant" according to Sir Alfred Gilbert.
When the statue was first unveiled the easily shockable Victorian public were duly scandalised by this display of public nudity. People mistook the statue for Eros, then became outraged that the staid yet generous Shaftesbury, president of the British & Foreign Bible Society, had been rewarded for his efforts with a statue of this 'frivolous tyrant'. In reaction to the popular mis-naming of Eros, the statue was then re-mis-named 'Angel of Christian Charity'.
As regards the direction of Anteros's arrow, it should properly be pointing towards Shaftesbury Avenue, as suggested, as a nod to the earl. Some have suggested that its positioning was also a sly bit of dirty visual punning on the burying of shafts in Shaftesbury, but this was probably not intentional. When Piccadilly Circus was remodelled to ease traffic congestion the statue was moved and its direction changed; old photos show it facing a number of different ways.