Metaphorically speaking, they are memories we hide away - our mistakes troubles
They could be disguised as a book or a letter While covered in dust a simple blow can create a stampede
Most closets have doors Some have locks But few have nothing - no barrier of protection
The people with these are the strongest Though they try to hide their skeletons, they are not afraid to put away that sweater and save it for another day.
In the last stanza, the metaphor of "save that sweater for another day" has greater meaning. It means that someone is strong enough to ignore their skeletons/secrets at the current time.