Schacter, D. L., Chiu, P. C. -Y., Ochsner, K. N. (1993). Implicit memory: A selective review. Annual Reviews of Neuroscience, 16, 159-182.
Memory is not a unitary phenomenon. Some memory processes are driven by conscious effort to bring to mind previously encountered information (declarative memory). Similarly, we might consciously try to recreate previous experiences, recalling where we were, what we were feeling, what we were sensing, etc. (episodic memory). These are explicit memory processes; whcih I think of as memory of. (I have a memory of an episode in my life, or an explict memory of a list that I learned.)
Other times, though, memory is apparent without conscious effort, and without any explicit effort either during encoding or retrieval. This is memory for; our knowledge of how to do things, contrasted with the propositional knowledge above (“knowledge that”).