Use a colon after an independent clause to introduce a list of particulars, an appositive, an amplification, or an illustrative quotation. from Elements of Styles

Your dedicated whittler requires: a knife, a piece of wood, and a back porch.

Understanding is that penetrating quality of knowledge that grows from: theory, practice, conviction, assertion, error, and humiliation.

Your dedicated whittler requires three props: a knife, a piece of wood, and a back porch.

Understanding is that penetrating quality of knowledge that grows from theory, practice, conviction, assertion, error, and humiliation.

Join two independent clauses with a colon if the second interprets or amplifies the first.

But even so, there was a directness and dispatch about animal burial: there was no stopover in the undertaker's foul parlor, no wreath or spray.

A colon may introduce a quotation that supports or contributes to the preceding clause.

The squalor of the streets reminded her of a line from Oscar Wilde: "We are all in the gutter, but some of us are looking at the stars."