Essentially Caius cloned and made into a Guard instead of a Volturi proper. It's subtly done, but if you look at Caius's distinguishing traits (violent, wants to kill the Cullens, no-powered lame-o) and Felix's distinguishing traits (violent, wants to kill the Cullens, no-powered lame-o) it's not difficult to see the similarities. Seriously Meyer, you couldn't have made him more original?
He seems to also bear a resemblance to Aro as he is cheerful sometimes like when he is killing someone. His appearance is also compared to Emmett's. The reason Aro keeps him around is because of his strength which ALL meyerpires have so keeping him around is stupid. However, this probably escapes Aro's notice as he is too busy engaging in lengthy, anti-climatic debates.
(The third sentence of the above paragraph is incorrect because Felix does not have the same strength as a normal Meyerpire, but is in fact supposed to be the strongest vampire, therefore making him physically stronger than all other vampires, which means that he can beat up other vampires and kill them, therefore making him useful to Aro. So people think that he may also be useful to Demetri.)