Definition from Wiktionary, the free dictionary
- (transitive) To fasten with a button or buttons.
- Button up your shirt cuff. It has come undone
- (intransitive) To fasten all the buttons on a coat, or similar item of clothing, to keep warm.
- Button up well. It's freezing outside today.
Usage notes 
- The object in 1 can come before or after the particle. If it is a pronoun, then it MUST come before the particle.
to fasten with a button or buttons