What is the secret about? Another child from a previous relationship just pops up in your life after she knocked on your door with a baby in her hands? Or you understood that he stands behind the famous unreleased bank robbery 15 years ago and he is not sharing with you where the booty is? Or you understood that he changed his sirname a decade ago from Dickhed to Smith? You see, it really matters what the secret is about :)))
It sounds like the secrets might have been from a time before the marriage. If that’s the case, the truth about his past probably doesn’t change anything about the man you know and fell in love with. If you allow yourself some time to adjust to the new information, you may find it doesn’t change your feelings about him and the relationship can move forward. Or there may be some compromise that can be reached. If the secret comes from a time after you were a couple, then trust may be an issue and will need to be repaired.
I definitely agree with KarmaChamaleon. Gauge how much you you will be able to take and how whether you'll be able to handle it. Only you know what your tolerance lvel is like. Some serious internalization needs to happen because after you made your choice, you can't keep bringing his past up. If you stay, don't nag him about it, put it in the past. If you leave, then it shouldn't be a major factor in your life anymore.
It depends on how bad this secret is. If he went to prison for murder or abuse, I'd run for the hills. Lesser crimes like stealingor breaking and entering should make you feel a bit weary but shouldn't be a death sentence. Anything less shouldn't be too problematic. Just let him know that he hsould've been honest with you from the start and go to onseling if you need to.