Proxy is kind of the slang name for the brushes that are specifically designed to get in between the necks of teeth. It's taken from the term inter-proximal, which means "between the necks of the teeth". This tiny compact brush fits snugly between the necks horizontally. If your dentist ever put splinted crowns (crowns that are attached to one another) in your mouth, those splinted crowns are actually designed to allow this brush to slip in between the gum line area below the contact. Proxy brushes are great at mechanically pushing bacteria and food out of the gum area to prevent future inflammation.
It’s important to note that a proxy brush shouldn’t be used on natural teeth because it could open a contact area and create a dark triangle. There’s actually a name for this; it’s called “black triangle disease”. Unless you’ve got splints, stick with floss.