According to the Court in Roe there are two "compelling" points in a pregnancy. They are the end of the first trimester and the point when the fetus becomes viable.
In this case, the Court had to balance two important rights. These were the woman's right to do what she wants with her body (her right to privacy) and the right of the fetus to live. The Court said that up until the end of the first trimester, the only interest that the state has that is compelling enough to regulate abortion (to limit privacy) is the health of the mother. Up to that point, the state can only put regulations on abortion if they are meant to protect the health of the mother. These would include regulations about making sure abortions are done by licensed people in licensed, safe facilities.
Then, when the fetus becomes viable, the state has a compelling interest in protecting it. At that point, a state may prevent all abortions unless they are needed to "preserve the life or health of the mother."