Yes and no.
Women have days that they are fertile and not really fertile. The thing is that we don't know when those days are. We can try to predict when we are fertile, similar to how we would predict when we should get our period, but most women do not get their period on that exact day that they expect to. That means that they might not be fertile on the days that they expect to be fertile either.
Also, fertility is not as obvious as having your period. It does not take much to know whether you have your period or not, but most women have no idea when they are at peak fertility. It is even possible for women to get pregnant if they have unprotected sex during their period!
Also, sperm can live in the vagina for a few days. That means that if a woman has unprotected sex a few days before she is at peak fertility, the sperm might might still be in there a few days later when she is at peak fertility.
This means that women should always assume that they are fertile and use protection every single time (the pull out method does not count!). Even with protection, there is still a small chance of getting pregnant, however. In many cases more than one form of birth control can be used at a time.