Felony convictions are the serious offenses. Misdemeanors are relatively trivial. A speeding conviction, for example, is not what they are interested in.
On of the reasons for the professional schools concern is that a felony offense may, possibly, lead to denial of licensure. The denial is not automatic, but will be considered by the licensing board in the state you want to practice in.
If you do have a felony conviction, in your own interest it is best to be up front. I knew a student who had a conviction for armed robbery with a drug involvement; he served jail time. When he applied to medical school, he told them about it. He also had a very supporting letter from the judge who sentenced him, who thought his turnaround remarkable. He is a licensed physician today, a graduate of a US medical school.
