avant-hier means “the day before yesterday”

More examples

Il a plu avant-hier soir.

It rained the night before last.

A calendar page with one full day between it and today.

il y a deux jours: Referring to two days ago in casual speech.
deux jours plus tôt: Referring to an event two days before a specified time.

Signifie le jour qui est deux jours avant aujourd'hui.

The French compound joins avant, from Latin ante meaning "before," with hier, from Latin heri meaning "yesterday."

As an adverb, avant-hier normally appears without an article, as in "Je l'ai vu avant-hier."