Autobiographical memory gives us our identity.
Among the many different types of memory there are, it is autobiographical memory that tells us who we are, and what kind of people we are.
We judge ourselves by what we remember having done or not done. We recall how we reacted or behaved with other people, and believe this gives us an insight into our personalities. In this way it is memory which creates what we perceive as our identities.
If we could not remember the past we would have nothing with which to compare our pleasure or pain. We would not be able to recall how we behaved in the past or what we had done. We would therefore not be able to assign to ourselves any kind of personality or identity.
Imagine being stuck in the present, with no concept of who you are. That will show you just how important memory is to you and your self-identity.