In 'homophilia', 'homo' could signify a shortened form of 'homosexual'.
Thus homophilia could have two meanings-
1) supportive, brotherly friendship towards gays and lesbians, or
2) non-sexual love between two men or two women.
Broadly, it means an open, non-judgemental acceptance towards gays and lesbians, or, alternatively, towards the expression of non-sexual warmth and intimacy between people of the same sex. It is the opposite of 'homophobia' - the fear or hatred of all things gay.