Learn Italian: Noi sappiamo i segreti, ma non glieli sveliamo. - We know the secrets, but we do not reveal them to him.

It is a combined double pronoun. The first part glie- stands for "to him" (the indirect object). The second part -li means "them" (the direct object, replacing i segreti). When gli (to him) combines with li (them), they fuse together with an extra "e" to form glieli.

If glie- means "to him", how would we say "we do not reveal them to her"?

The sentence would look exactly the same: non glieli sveliamo. When combining with a direct object pronoun like li, both gli (to him) and le (to her) transform into the exact same prefix: glie-. You have to rely on context to know if it means "to him" or "to her".

Why use sappiamo for "we know" instead of a form of conoscere?

Sapere (conjugated here as sappiamo) is used for knowing facts, pieces of information, or how to do something. Conoscere is used for being acquainted with a person or a place. Since secrets are pieces of information, sapere is the right choice here.

Why is non placed before glieli?