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.