Standard mattresses are between 9 and 12 inches deep. So deep mattresses are anything beyond that. Typically, deep mattresses will be 13 to 18 inches thick. But some mattresses can go all the way up to 24 inches thick.
The depth of the pockets of a mattress protector (and a fitted sheet) determines the depth of the mattress it will fit. So if you have a deep mattress, look for a protector with deep pockets. Most protectors will say how deep of a mattress they will fit.
So you’ll need to measure from the base to the top layer of your mattress to determine its thickness before you shop. If you have a mattress topper or mattress pad that’s going to be under the protector, you’ll need to include that too.