Learn Italian: Questa non è una premonizione e non c'entra niente, glielo assicuro. - This is not a premonition and it has nothing to do with it, I assure you.

This is a perfect example of the pro-clausal lo. Instead of replacing a specific masculine noun, it replaces the entire preceding idea: the fact that "this is not a premonition and has nothing to do with it." While English might say "I assure you of this" or just "I assure you," Italian cleanly packages the whole statement into the pronoun lo.

The translation says "I assure you," but doesn't glie- usually mean "to him" or "to her"?

It does, but it is also used for the formal "to you" (A Lei). When the formal indirect object pronoun Le combines with a direct object pronoun like lo, it changes to glie- to form the single word glielo. If the speaker were talking informally to a friend, they would use ti, making the phrase te lo assicuro.

Why does assicurare take an indirect object for the person being assured?

Because the structure in Italian is assicurare qualcosa a qualcuno (literally "to assure something to someone"). The "something" is the direct object (the pro-clausal lo), and the person receiving the assurance is the indirect object (the gli- part of glielo).

How does c'entra translate to "has to do with it"?