My definition: The idea that men and women are *literally* equal, and should have equal roles in determining *all* aspects of family life. This is far more mild than that of radical feminism, and probably more mild than mainstream feminism.
I believe men should have priority in determining family direction because it has been that way since we crawled out of the river vallies, and there is probably a good reason for it being like that - in any case, the collective unconscious has incorporated this idea so deeply that to monkey with it is dangerous. This implies that 1) women are more important for actually raising children 2) men are more important for providing for the family, both in terms of abstract direction and material needs. This does not mean that women should receive less for equal work, or be prevented in any legal way from doing X. One should let family and employment relations naturally evolve without input from the government.
It may actually be that the majority people prefer the emerging world, but I am sure it will be sterile, violent, and miserable, as the individual smoothing effects of nulling out gender differences show up in collectivist upheavals (the natural result of tinkering with - no irony intended - Mother Nature). The basic idea is - the more uniform you make individuals, the more likely they will form into irrational destructive collectives.