There's actually more than two sides, as most people think that abortion should be legal in at least some circumstances.
So let's say that a woman is pregnant. She decides that she doesn't want to carry the baby to term. Legally, under what circumstances should she be allowed to end the pregnancy? Some people would say "never" -- those people call themselves pro-life or anti-abortion. Others would say it's okay to have an abortion if the pregnancy happened because of rape, incest, or if it threatens the life of the mother. Many others would say that it's her choice to make and the government should stay out of it. Those people would be called Pro-Choice.
Where people fall on the spectrum has a lot to do with how authoritarian their parents were. If you had parents who beat you, for example, you're more likely to be pro-life. If your parents didn't beat you, you're more likely to be pro-choice. Also, it depends on how you see sex. If you think sex should only occur within marriage, and only to have a child, you're much more likely to be pro-life. Further, if you're a stay-at-home mom, you're more likely to be pro-life, and to resent women who can choose when to schedule their children. If you believe women should work and have careers, you're more likely to be pro-choice.
Weirdly, a lot of people will say that they are against government, but then they think government should be able to force women to carry a pregnancy against their will. Go figure!