You ovulate a week to two weeks after your period (depending on your body and cycle). If you are on the pill, you will ovulate during that time, but you are on the pill.
How the pill works is that the extra hormones in your system alter the way your cycle works: you will still ovulate, but even if you get pregnant you will still have your period about two to three weeks later (depending on when you ovulated). Some people have moral issues with that. Some people call this type of birth control abortifacient, meaning it forces you to lose the fetus. Some people believe that certain birth control pills prevent you from ovulating, but as far as I know, no birth control pills do that, they only force you to have your period every 21-28 days by putting your body on a regimented dose of hormones.
If you ask your doctor about it, if your pill is an "abortifacient" s/he will most likely avoid the issue, as my doctor did, as well as my friend's doctor, and even a third doctor of another friend. It's a sticky issue and honestly, a lot of doctors breeze over how the pill works (not even in relation to being an abortifacient). I see a lot of posts with a lot of confusion on "can I get pregnant if..." and "how do I take this during..." it seems that a lot of doctors aren't explaining how the pill works to a lot of their patients, they just want to tell you "you can't get pregnant, now take it". For the first few months that I was on the pill my husband and I were constantly nervous that I would get pregnant. But I have since learned about my cycle and what happens when, which hormones cause it and I know it is very unlikely to get pregnant on the pill for several reasons (even though it can still happen).
If you are on the pill, you most likely will not get pregnant, no matter when you have sex, because the extra hormones you are ingesting alter your cycle to make you have your period every 21-28 days, regardless. The pill is only 99% effective (one of my best friends got pregnant with her first son while she was on the pill), but that's a small gap.
There are other methods of birth control that do not involve inducing your period, if that is a concern for you, that are as effective as the pill.