These are words that I considered tossing into a 教科書に載っていない post, but then I figured it be more fun to do them like this.
裏, not to be confused with the homonymous 浦 from 津々浦々, has tons of meanings, but the common thread that they share: you can't see the 裏 from the front.
表, which you can find in 表面, 表現, and 代表, has an equal abundance of interpretation and represents the opposite of 裏. It's the visible surface.
You might remember both of these from 表裏一体.
They work really well for talking about buildings and locations (駐車場は裏にあります) and I hear them a lot at work, where 表 is the part of the bakery that the customers frequent, and 裏 is where the baking gets done (「表の掃除終わりましたか。」とか「裏から鉄板持ってきて。」).
But where you can hear it and use it most often is in today's cultural trivia:
裏か (うらか;uraka) as it gets abbreviated in speech, is a system of dividing people into two groups. I want to call it a kid's game, but then... it's not a game, though it often precedes games, and much like じゃん拳 (じゃんけん；janken), everyone in Japan does it, regardless of their age.
Whenever you have a situation where you need two groups, or two teams, you can find people doing 裏か表, which works like this: 裏, as it's meaning implies, refers to 手の平, the part of your hand that can't be seen from the front, so... your palm. 表 in this case is 手の甲, the back of your hand. Everyone stands in a circle, puts a hand in, and then everyone (or at least SOMEONE) in the group chants 「裏か表！」 while shaking/flipping their hand back and forth between the two states of hand-existence.
On the final chanted syllable, everyone picks a side and thrusts their hand out, showing either 裏 or 表. If the numbers of people who chose each are approximately even, then 裏s form one group, 表ｓ form the other. And if the numbers are way off, the process is repeated. Just like じゃんけん has あいこでしょう, when you have to do it again, there's a different chant. What that chant is, however, is subject for disagreement. The kids that I learned it from always said 「手、手、のって！」 Yuri says simply 「っせ！」 There are even little kid versions that get longer and ridiculous, 「裏かオモ、てんぷら、ハンバーガー。。。」 and on into あほ臭い territory. Have people in other parts of Japan heard other versions?
裏 and 表 can also be linked to ideas of 本音 and 建前, as well as martial arts, but those are subjects for other posts.