My son's (formerly my grandparents') house has counter-to-ceiling wooden, glass-front cabinets on one wall with under-counter huge hard-to-open drawers and a flour bin down to the floor. The actual counter/work area is only a small open space between the tall cabinets and is made of wood. There is no other counter space in the very small kitchen. My grandmother had used a VERY small kitchen table wedged in near the back door as her place to mix and dice.

My son cannot figure out how to remove the tall wall cabinets. He doesn't see any screws or nails and wonder if the cabinets were glued in (websites say in that time period wall cabinets were "fitted in" or "built in," whatever that means). How easy would they be to remove (without ripping up the entire wall behind them)? Does he need a professional for this?

They were built in. That means 1 x 2's glued and nailed to the walls, tops, bottoms, and vertical dividers added, face frames fitted on the front, and then shelves and doors.

Remove the doors by the hinges and then hit the rest with a sledge hammer, and the 1 x 2s with pry bar and hammer. Use a shingle against the wall so that you don't damage the plaster on lath, although some of it will come off anyway.