You're at your potter's wheel. You make the bowls. (Or vases. Or plates. Or jars. Or most anything.) The clay is nice and responsive to your touch, and you succeed at making the form you intend. Still, the odds are good that you needed to leave some extra clay at the bottom of the piece (the "foot"). A little extra at the bottom helps you lift the piece off the wheel without distorting it. It gives the wet clay a sturdier base.
It does not look very nice, though. Hiding inside it is the true profile of the foot. These two bowls were thrown the day before I took the picture. They are firming up, but not dry. Call them "leather hard."
Now I put one back on the wheel, upside down and as exactly in the center as possible. I "trim away" the excess clay. The bowl turns and I move various sharp tools over the surface to refine the form, creating the finished foot that is longing to be revealed. I remove it from the wheel and put on the next bowl. When they are finished (though still raw clay, not having been heated in the kiln and not having been glazed with color), they look quite a bit different.
The one on the right is the same bowl as the one on the right in the upper photo, the one on the left the same as the one above on the left. Quite a difference, isn't it?
When I "threw" the bowls, which is the term for making them on the spinning potter's wheel, I left a nice thick bottom, about 3/4", with the intention of making a raised foot. A foot like this, narrow and well defined, raises the bowl from the table surface, showing its graceful profile to advantage. A shorter, wider foot would give the bowl a more utilitarian look. It's all valid, all choices I have to make before I slap the clay down onto the wheel. I plan this sort of thing, in fact, while I'm weighing out and kneading up the amounts of clay I will be using that day.
So now you know what it means to "trim a pot!"