Either today is Monday or Tuesday contains the correlative conjunctions either/or. Peters in The Cambridge Guide to English Usage (p300) lists correlatives as one example of grammatical redundancy. She defines redundancy as:
...a general term referring to where the same grammatical meaning is
expressed more than once in a clause or sentence.
She says that the use of correlatives makes for 'good style', and notes that redundancy such as in the inclusion of either in the OP's example:
...is particularly useful in spoken discourse because speech is a
linear form of communication that disappears into the air waves. The
repetition or underscoring that goes with redundancy helps ensure
that details of the message don't get lost.
So, to complete the OP's sentence:
"Either is redundant in above example. Its absence in the sentence will not make any difference in the meaning of the given sentence."
(But its inclusion serves to underscore the alternative nature of the
two elements Monday or Tuesday.)
Another term which denotes the inclusion of superfluous words is tautology. Tautology refers to the repeated expression of the same idea in a single phrase or predication (Peters, 335):
For example the free gift used in advertising copy; or the phrase in
the classroom context where "context" adds an unnecessary
superordinate to the preceding adverbial.
Pleonasm is the term that subsumes redundancy and tautology (Wikipedia links).
