Use when referring to someone you know directly, highlighting the personal nature of the relationship. I'll introduce you to an artist of your acquaintance to discuss the gallery.
Pro Tip 2/3
Not Acquaintances
Do not use for people you've merely heard of or seen online but haven't interacted with personally. Celebrities I admire aren't people of my acquaintance since we've never met.
Pro Tip 3/3
Formal Contexts
Fits best in formal or semi-formal conversations, as it may sound overly formal in casual settings. Is there a scholar of your acquaintance who could speak at our conference?