In mathematics, a constructive proof of existence leaves you with a method to actually find an instance of the object whose existance is being asserted. By insisting on constructive proof, existence becomes a stronger notion.

A constructive definition is a definition of (a) mathematical object(s) that can be constructively proved to exist.

At least, this summarizes my understanding of an article on L. E. J. Brouwer in a weekly magazine 20 years ago.