Memories are formed and stored in different parts of the brain. Here's a brief overview:
The hippocampus, a structure found on each side of the brain, is where explicit declarative memories are formed. These are memories of what you know and what you know how to do. However, the hippocampus is not where these memories are stored and maintained.
Implicit memories, the subconscious memories, are formed and stored elsewhere in the brain, mainly by areas like the cerebellum and the neocortex, which is the outer shell of your brain.
The process of learning something new and then it becoming more or less reflexive involves a migration of the information in the brain. The sequence of electrical firing, much like a script for a movie or the notes on a sheet of paper for a particular musical piece, is transferred off to a different brain area, such as the neocortex.
So, while the hippocampus is crucial for establishing new memories, the long-term storage of these memories happens in other parts of the brain.