Determiner ‘either’ means any one of those terms. ‘either’ can be used as a pronoun, a determiner or an adverb.
Example: Either of them will visit the Nairobi International show.
Determiner ‘neither’ means not one of the two. ‘neither’ can be used as a conjunction with ‘nor’, or as a pronoun.
Example: Neither of the guests turned up.
Learn more about how to use so, too, either and neither