To remain is to stay in the same place or situation. You can remain at home instead of going out to the movies with your friends, but that doesn't mean you won't remain friends.
If things remain the same, they don't change, and if your family remains in the same town, they don't move. When something is left behind, it also remains: "All that remains of my party is a bunch of deflated balloons." In the fifteenth century, remain was a noun too, meaning "people or things left over or surviving." Today we use remainder instead.