Covering something suggests obliterating it or hiding that which we do not want others to know about us. Burying something in the earth in a dream suggests hiding a misdeed of some sort.
Psychological / emotional perspective: Covering over anything signifies making the best of or preserving what we have, perhaps ensuring that shortcomings are not recognized.
Material aspects: It will depend what and how we are covering in dreams. Covering an article in brown paper portrays the need to be pragmatic while covering an altar signifies an act of devotion. Covering a chair suggests added comfort while covering up our actions suggests we are aware of opprobrium.
(See Blanket; Envelope; Irreligious; Shade; Wrapping)
Dreams about a cover represent protection or hiding. Because a cover can make something more beautiful than it would otherwise be, this dream may be about your attempt to fit in by hiding your uniqueness. Consider what is being covered.