It's just giving a vector a name. It also names ê₂. These particular names are very standard and familiar to most people who've met vectors before.

You can look at those vectors and see that the position of the 1 is the subscript, without explanation. The ^ could do with an explanation that it means unit vector, but if you've met vectors before you likely know that (maybe that's elsewhere in the book, but a quick search didn't find it).