What does "Did you save room for dessert?" mean? I'm an English learner. I don't know what this sentence means, especially the "save room" part. Please describe its meaning for me.
"Save" is being used to mean "put away for later". "Save" is often used this way when referring to money "Saving up to buy a car", or if someone wants you to share "save some for me".
"Room" is being used to mean "empty space". When entering a large gymnasium, one might say "there is a lot of room in here".
So "Did you save room for dessert?" is literally asking if you kept some space empty in your stomach for dessert, but it usually means they are offering you dessert.
It's a tactful way of offering because it allows someone to say "no, I'm full" if they don't want dessert.
It means, "Are you too full to eat dessert?"
Here is a definition from The Free Dictionary:
To refrain from eating too much so that one still has an appetite for something else later on.