Eye-stripe

Dama. [i.e., the dama gazelle] Horns hooked forward at the ends; body white; dorſal and eye-ſtripes tawny.

MALIMBA BEE-EATER. […] Cinereo-violaceous Bee-Eater, sanguine rose-coloured beneath, with black eye-stripe, white throat, and two lengthened tail-feathers.

The eye-stripe is exactly that: a stripe through the eye. When present, this is a dark line that usually extends from the bill back through the eye. On some birds, it extends just from the eye back, leaving the lores (the area between the eye and the bill) pale and unmarked.