To interrogate is to ask someone a bunch of questions. Usually, it’s the police, FBI, or other law-enforcement officials who interrogate suspects, but your father-in-law may interrogate you about your career plans.
Interrogate comes from the Latin prefix inter-, “between” added to the Latin verb rogare, “to ask.” To interrogate someone is not just asking a few polite questions over a cup of tea. When you interrogate someone there is usually a method to the questioning with a specific mission in mind, like determining a criminal's motive or where she stashed the loot. Your college entrance interview may feel like an interrogation, but their mission is really just to get to know you.