I can give several levels of explanation to this. Basically, there are different types of memory. It is enough to make a distinction between long-term memory and working memory. When you first experience something, it enters your working memory. If it is important, the memory becomes consolidated. There is a biological process underlying this process and it is called long-term potentiation. Essentially, it means that when you have an experience certain neurons in your brain fire a signal. Overtime as your experience grows stronger, then the firing repeats and that leads to the neural correlate of your memory. Most researchers agree that the part of the brain called the hippocampus is probably an important neuroanatomical correlate of memory.