Etymologically, 'homophile' is derived from two Greek words - 'homo', meaning 'the same', and 'philos', meaning 'friend', or possibly 'philein', meaning 'to
love', or 'to be dear to'. Greek uses 'eros' to signify 'sexual
love', so philein should be taken to signify non-sexual
love between friends or members of the same family, e.g. brothers.
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.