A big eye refers to an eye of at least four spaces in the context of capturing races. A big eye has more liberties inside the eye than the number of points
Also, a big eye has an advantage vs. a smaller eye in a capturing race. See Big Eye - Small Eye.
See Four is Five and Five is Eight and Six is Twelve and Nakade Liberties. Be aware that big eyes can be small in the corner.
If in the corner and with cutting points, big eyes can be not so big; see famous problem with many captured stones and still a dead shape). -tderz
See also the Eyes Collection.