If there's one thing I especially dislike about the Japanese language, it is the obscene amount of counters that exist. A counter should be thought of as "a word used to demonstrate amount for a specific set of objects." For example, in English one would say "There are five cars," while in Japanese one would say "kuruma ga go dai arimasu." Let's dissect that sentence, shall we?
Kuruma (car) ga (particle indicating subject) go (five) dai (counter) arimasu (verb meaning to exist).
In this sentence, dai is the counter. This counter is used for vehicles and machines. That's all fine and dandy, except for the fact that there are dozens of counters for every conceivable type of object in existence. I miss English for this fact: We have one, and first, and that's really about it. No need to get any more specific. In Japan, there are counters for:
Small Objects: ~ko
Birds and Rabbits: ~wa
Long, Thing Objects: ~bon/pon/hon
Floors (of a building): ~kai/gai
Rankings (1st, 2nd, etc): ~ban
...and more! You can find a more complete list here.
I am still learning all of the counters, so when in doubt I fall back on the "general" counters, which can be understood by most people:
1 = hitotsu
2 = futatsu
3 = mitsu
4 = yottsu
5 = itsutsu
6 = mutsu
7 = nanatsu
8 = yattsu
9 = kokonotsu
10 = too