Basically, complimentarianism is the belief that men and women have gender roles in the church. Egalitarianism is the belief that men and women are completely equal when it comes to gender roles. The former can be misinterpreted as misogynistic (right word?), but here is a complementarian's view on marriage regarding a question I've wondered about before - what should a man, who believes he's called by God to a ministry, do when his wife is NOT on board with the ministry:
You are called to a self-sacrificial headship in your marriage. This means you love your wife, and you do what’s best for her, even to the point of crucifying your own ambitions, your own callings, and even your own life (Eph. 5:25-30). Don’t put your wife in the situation in which she must choose between loyalty to you and fidelity to what she believes. If that means serving the Lord in some way other than the pastorate, so be it. Your marriage is more important than your ministry.
Pretty strong. Agree?