It's the glu that's important in an agglutinative language.
The glu: it's used to stick words together to make new ones.
All languages tend to do this, of course, but the usual habit is to squish the words a bit as you do it. This both makes them easier to say, and can be much quicker. For instance, if you want to say I am in the past in English you say I was. It really does save time. That way of doing things is called fusional. In an agglutinative system the bits glued together aren't changed in any way at all.
It makes agglutinative languages easy to understand, because when words get recycled their meaning remains obvious. This trait has been seized upon by the developers of both Esperanto and Klingon.
It follows that, on the whole, agglutinative languages tend to be very regular. Japanese, for example, contains only a couple of irregular verbs, and Turkish and Quechua have none at all. (As a learner of languages, I regard this trait as a fine, kind, and reasonable thing.)
As far as I know, all languages have both agglutinative and fusional traits. German, for instance, has a habit of sticking its nouns together unsquished, but has quite complicated and arbitrary ways of telling you what each noun is doing in its sentence.
It's really almost enough to make you wonder if languages aren't designed as much to stop people understanding them than as a means of communication.
Word To Consider Today: agglutinative. This term was coined by Wilhelm von Humboldt* and comes from the Latin agglutinare, to glue together.
*This von Humboldt was the brother of Alexander, after whom (indirectly) the Humboldt penguin was named.
I bet their parents were dead proud.