Memory is not a thing that you can measure. There is no single place in the brain where memories are stored or where remembering happens. You can’t take an MRI of your brain, point to your memory, and say, “My, what a good memory I have!”
Memory is better thought of as a collection of behaviors that you use to organize information in your mind. So, when someone says that they have a “bad memory,” what they are really saying is that they don’t have a good process for storing and retrieving information. While there is some link between intelligence and memory ability, memory is mostly a learned skill and you can get better at it with practice.
Exercises designed to improve your memory are not trying to enlarge or strengthen any particular part of your brain. Instead, they are teaching you new behaviors and skills that can be used to organize information in your mind and improve your ability to recall this information rapidly and accurately.