Although this word was made up in order to be a contender for the longest word in English, it can be broken down into smaller chunks in order to understand it. Anti- means that you are against something; monopoly means the exclusive control over something; geographic is related to geography; and the remaining part has to do with nationalism. So this word means something like 'a nationalistic feeling of being against geographic monopoly,' but you can see that it doesn't have much sense.
This word is the longest alphabetically spelt word in English. The meaning of the word is ''down with the capitalism" and we can deduce that by breaking the word into its parts.