To remember is to recollect, or to call upon your memory. Remember that time you fell out of your tree house and bonked your head? No? Go figure.
There are many shades of meaning of remember, but at its core it refers to the act of recalling or thinking back. You can remember something fondly, like your first kiss, or you might remember something suddenly, like when the smell of tar brings back the time your bicycle wheel got caught in a pot hole and you fell off. To remember someone means you show appreciation, like when the Oscar winners try to remember all those names.