Language prides itself on precision. It is a tough medium because language will never be able to fully recreate abstractions. For example, when we speak of "beauty" or "pain," different constructions and notions will cloud the mind. The symbolic nature of language helps to create this lexical ambiguity. Any time we can find precision in language, it should be noted.
The statement of "Today is Monday" makes more sense. The sentence clearly establishes the subject of the sentence. When finding the verb of the sentence ("is"), the subject becomes "Who or What 'is?" Thus, the idea of "Today" being the subject is clearly established. The use of "it" is not necessary. Therefore, clarity is achieved with "Today is Monday" as opposed to "Today, it is Monday."
"It" may be a personal pronoun or what is called a "dummy subject it" that substitutes for the actual subject of a sentence: "it" substitutes for "today." In fact, in both uses (personal pronoun and dummy it), "it" is used to substitute for the subject. For example, if we were talking about "Today" as a subject such as "Today is a bad day" or "Today is going to be a challenging day" or "Today is filled with appointments," then we could use "it" as substitute for "Today." The sentence "Today is Monday" is grammatically correct and clear. Saying "Today, it is Monday," employs both the actual subject ("Monday") and the dummy it subject substitute. Thus this structure is grammatically incorrect since duplication of the subject is not correct English grammar. For instance, in English, duplicating the subject by saying "The dog, it is fuzzy" is recognizably ungrammatical, and the same is true for the duplication of the subject in "Today, it is Monday." In short, "it" may not be used as a duplicate subject as in "Today, it is ..." but "it" may be used as a substitute, dummy, subject as in "It is Monday." For the purpose of correct grammar and syntax usage, it is correct to say, "Today is Monday" or "It is Monday" but never "Today, it is Monday" because it is never grammatical in English to use duplicate subjects: the subject "it" duplicates the subject "today."