Finnish has 15 noun cases, but it's probably better thought of as 4+6+5 cases. The first 4 are pretty straightforward, except for the partitive, which is kind of a catch-all case. The middle 6 correspond to certain spatial relationships. Very roughly you can imagine these as {inside, outside} × {unmoving, moving closer, moving further}. Huone = room, huoneessa = in room, huoneen = into (=moving closer to the inside of) room. That kind of stuff. The last 5 have niche, special uses. That's how I mentally imagine them at least, there are a lot of details you only pick up by reading a lot.
The trade-off is that Finnish has virtually no prepositions, which English has a lot of, and which are similarly very confusing for beginners and even intermediate English speakers. There are a few post-positions, but even these are mostly things you can pick up by ear.
Verbs have a similar story. If you've ever learned Latin, Russian or Spanish you'll feel right at home with Finnish verbs, which pack a lot of info into the conjugation, but with the benefit of requiring fewer actual words per sentence.