Minecraft custom maps are a very popular thing to do in Minecraft. There are many different kinds of map and they are split into different genres. The main genres are adventure, puzzle, parkour, simulations or any combination of them. There are many different maps, but there are only a handful of very popular and successful ones.
Adventure maps are the most like modern video games. This type of maps that tell a story. The most popular one are made by Hypixel. Hypixel is famous for making complex and beautiful maps with challenging enemies and a deep story line. With the new updates people can add custom sound files into Minecraft and it allows custom map makers to record them talking and let them communicate directly with the player.
Puzzle maps have you solve many difficult challenges that require lots of thinking. The most popular ones require you to have a friend to play with. Great examples would be 241 or it's better together. The multiplayer maps require a lot of teamwork and a deep understanding of the mechanics of Minecraft. As the puzzles get more frustrating the puzzles take longer and longer, but you get a rewarding feeling when you finish the game.
Parkour maps require a lot of skill and timing. They seem simple on the surface because your only objective is to get from point A to point B. The most infamous of them are TPC and T3C parkour, each of them having a hundred frustrating stages for you to jump, duck, and dive through. You need to time your jumps and aim your landing with precision. The harder ones usually have moving elements and special powers that you normally don't get while playing the game. These maps are more fun to play with friends, so when you fall off a platform your friend is there to save you.
The simulation maps are different from the previous ones, but may have some of their qualities. Some of the stranger ones let you play Minecraft in Minecraft by building redstone computers, but they can also be as simple as putting connect four in Minecraft. There are also custom maps that imitate other games, like League of Legends. Race for wool maps are maps that let you compete against your friends with two teams that compete on two mirrored strips of land.
Many YouTubers play these games and have gotten famous and rich off doing playthroughs of these maps. Yogscast and Captain Sparkles have a full time job playing games just posting them on Youtube. I'll link some of the maps I mentioned above.
When you're finding custom maps from minecraft download at your own risk
The more reputable site is the Minecraft Forums otherwise you risk getting viruses.
These all require you to own minecraft to play. You can always look up playthroughs on YouTube.
The most revered map maker Hypixel's website: hypixel.net
Infamous T3C map:
http://www.minecraftforum.net/topic/344309-142parkour-t3c-tetrix1993s-3rd-obstacle-course-ver-311/
I just realized how lengthy this was. I might have to shorten it.
Mountains are my second favorite kind of biome and are have very interesting landscapes that let you have very high vantage points and the color scheme is very close to that of the taiga. 
