Correct spelling, explanation: to create an ordinal number form from a cardinal number we usually add the suffix -th to the word. Because of the fact that eight ends with consonant t we just have to add h at the end: eighth. We can’t omit the first h from eight, therefore eigth is a misspelling.

Definition of eighth:
numeral, the ordinal number between the seventh and ninth
It is my eighth day at new work and I like it very much already.
Jack got a bike for his eighth birthday.

Incorrect spelling, explanation: eigth is a wrong spelling because to create an ordinal number in most cases we have to add suffix -th to the cardinal number. This way ordinal number from eight is eighth (we skip the t since it is already there).