I won't be able to make the meeting vs I won't be able to make it to the meeting

The sentences are the same in meaning but differ slightly in construction.

Make has many senses, but the most relevant is probably "reach, attain" (12a), from Merriam-Webster.

Make it meaning to reach or arrive (often on time) is an idiom. Merriam-Webster in the same reference says "make" meaning "reach, attain" is "often used with it" (example: "you'll never make it that far"). Macmillan (British English) gives "make it" as meaning "to manage to arrive on time". There is also a sense (Macmillan again) "to succeed in a particular activity" (example "She made it in films when she was still a teenager.")

"Make" in the sense of "reach"/"arrive" is a transitive verb. "Make it" already has "it" as the direct object of make so you need to add another phrase such as "to the meeting" to explain what is being talked about. "Make it" is more often used without specifying what is being reached (e.g. "I can't make it.") but it's possible to add an indirect object as in "to the meeting". This may seem like a waste of words, but it's perfectly grammatical: that's just English for you.

In "make it", "it" is what Wikipedia calls a "Dummy pronoun" (there are many other terms such as pleonastic pronoun or non-referential pronoun). Wikipedia's article isn't very clear, but "it" without a referent is sometimes used in English where the object is vague or general (see this article on BrightHub for what's maybe a better summary). This gives the expression "make it", with its various related meanings ("arrive", "arrive on time", "succeed", etc). See also "I get it" (="I understand"), etc.