I was at my friend's house and I signed into my Xbox One account, but I hit remember password by mistake. I went home and changed my password. Can my friend still log into my account from his Xbox, since I signed in once?
After a password change any attempts to login with the old password will fail.
If you left your account logged in, then he will have access to the session saved locally on the XBone. He will stay 'logged in' until an action occurs that needs a connection. If the password isn't correct he will get booted out of that session.
I suggest asking your friend to un-tick the box, i'm sure he would oblige.