To be specific, "agglutinative" is an adjective that describes particular aspects of languages, but it may be attributed to entire languages if it is an overall general quality of them as a whole. What it means to be "agglutinative" is to go and carry out word-formation, and in more general usages of the term, marking of grammatical information on words by connecting multiple different units, known as morphemes, together, which express different overall ideas, and which are for the most part relatively independent from each other. This is as opposed to "analytic", which describes aspects of languages, and by extension entire languages, which rely on the usage of higher level syntactic structures involving words, such as word order, prepositions, and auxiliary/modal verbs, to communicate ideas, or "fusional" (often called "inflectional"), which is similar to the term "agglutinative" except that single morphemes may very well express multiple ideas together in an inseparable fashion, which may include word stems themselves, such as in the case of ablaut in strong (and mixed) verbs in Germanic languages.
The reason why Japanese is an agglutinative language is that it very strongly tends towards forming words out of many different suffixing morphemes tied together, which is shown in particular in the case of verbs (and stative verbs, that is, "i-adjectives"), where the only real fusional-type feature is the changing of vowels at the ends of verb stems in different usages. The only truly analytic aspects of Japanese are its use of grammatical particles, which are analytic because they apply to entire phrases, not just individual words as case markings like those in Finnish would, and because they can apply to other particles which in turn apply to other words.
The reason why Japanese is an agglutinative language is that it very strongly tends towards forming words out of many different suffixing morphemes tied together, which is shown in particular in the case of verbs (and stative verbs, that is, "i-adjectives"), where the only real fusional-type feature is the changing of vowels at the ends of verb stems in different usages. The only truly analytic aspects of Japanese are its use of grammatical particles, which are analytic because they apply to entire phrases, not just individual words as case markings like those in Finnish would, and because they can apply to other particles which in turn apply to other words.