Learn Italian: Il segreto, glielo sussurro all'orecchio. - The secret, I whisper it in his ear.

This is a structure called left dislocation. To emphasize the object (Il segreto), it gets moved to the beginning of the sentence. When doing this, Italian grammar requires a matching direct object pronoun—in this case, the lo combined into glielo—to resume the object right before the verb.

How exactly does the pronoun glielo break down here?

Glielo is a double object pronoun combining the indirect object gli (to him) and the direct object lo (it, replacing il segreto). Whenever gli combines with lo, la, li, or le, it changes its spelling to glie- and forms a single word.

Could glielo also mean I whisper it in her ear?

Absolutely. While the English translation says to his ear, glielo is also the required form for to her (the expected le + lo becomes glielo). In spoken Italian, it is also frequently used for to them, replacing the bulkier lo... a loro. You rely purely on context to know who is receiving the action.

Why is it all'orecchio instead of al suo orecchio (in his ear)?