Remembrance is when someone remembers things — your grandfather might have uncanny remembrance of his childhood, for example.
The noun remembrance is really just another way to say "memory." It's the process of remembering things that happened in the past. In Shakespeare's play "Hamlet," the character of Ophelia famously says, "There's rosemary, that's for remembrance." The smell of the herb has actually been shown to improve memory, and has historically been a symbol of remembrance. Early uses of remembrance had the meaning "keepsake or souvenir."