Nobody knows! We don’t know how memory works really, but we have a few ideas. Memory is super complex and truly amazing.
The hippocampus is involved in some way with memory making, and memory recall. We don’t understand the mechanisms underlying this well enough though.
Memory is probably stored across the brain but is not a single thing. Motion memory is stored in the motor cortex, visual memory is stored in the visual cortex etc
It is not known where semantic memory is stored, there is a semantic hub theory worth looking at on Wikipedia. Semantic memory is like the meaning of an object. For example, remembering what a chair is, and what it is for.
When you remember something simple, such as eating an apple, your brain is doing something so coordinated it is almost unbelievable. Your motor cortex is procesing the motion of your hand/arm and mouth, your visual cortex is processing the colour and shape, some part of your brain is recalling that is is food and so on. They all come together to form the memory.
What is amazing is that you can break down which bits of your brain are procesing in to smaller and smaller locations. For example, the location of the fingers area on the motor cortex and the mouth chomping bit are not the same place. The sensory input of taste, your mouths location relative to the apple, the feeling of the apple in your hand and mouth are all processed differently. Colour, size, shape are all processed in different places of the visual cortex. There is way more areas involved than these too, but you get the idea.
Despite the vast array of brain regions needed to come together to form a memory, you experience the memory as a single and unified. That is mind-blowingly awesome!
As a side note, the way memories appear to be stored and processed goes some way to explaining how they change so much over time. Chances are that some of your memories are just plain wrong, you don’t know which ones are a true representation of what happened, and which are not.
Sorry for the poor grammar and format, typing on the phone.