I think that this one might require a case-by-case ruling, which is what the DM is generally for. V2Blast does a good job of just pointing out the common English definition of a "free hand", but depending on how realistic the game is being run, there may be some things that you can do without a free hand.
For example, I can hold several bags of groceries, a phone, a waterbottle, and also use that hand to unlock and open a door, even though neither of my hands are free. But I probably couldn't reload a gun or do anything precise, and I certainly couldn't attack with a sword, at least not without dropping all my eggs. I might be able to make minor gestures to cast a spell, although not competently.