One of the things that made SMB3 such a hit, is how its worlds were laid out.
In previous Super Mario Bros games, there was no overworld map, you would simply go from level to level. Super Mario Bros 3 brought overworld maps into the Mario universe. This was idea was continued on in Super Mario World, as well as the New Super Mario Bros. series.
Each world also has its own name (describing that world's theme).
These names differ from the first and second release of SMB3.
The second version simply added the word "land" to the end of each world's name.

(Click on any of the world images to view the full-sized image)

World 1: Grass Land/Grass Land

World 2: Desert Hill/Desert Land

The far right part of this map shows a hidden Fire Bro. Mini-Level.
You can get over there using the Hammer Item. Just one of the ways the maps were interactive.

World 3: Ocean Side/Water Land

Ocean Side, such a nice name. There's a boat in this world which you can access if you use a hammer item to destroy the rock that is blocking the dock. Once on the boat/canoe you can visit two island, which have Toad Houses and Spade Panels.
As a kid this was my favourite world, I thought the boat was simply amazing.

World 4: Big Island/Giant Land

This world is a fan favourite. Enemies are BIG!
Big Goombas, Big Koopas, Big Pipes, Big Bricks!
This was my brother's favourite world growing up.

World 5: The Sky/Sky Land

The map in the game doesn't look exactly like this, the left and right sides aren't connected.
You enter the spiral castle on the left side, and end up in the sky on the right side.
You can even see the left (grass side) all small in the corner of the right part.
This world is also the world which contains Goomba's Shoe, the only one in the game.

World 6: Iced Land/Ice Land

A fun slippery world. Mario's fireballs can finally destroy ice! Well, some ice.
You can also pick up a Hammer Bro. Suit here.

World 7: Pipe Maze/Pipe Land

Good Ol' Pipe Land. Has levels which are indeed filled with Pipes.
Level 8 in fact is just a big pipe maze.
Also, the first fortress is quite a classic. The coin fortress.
Don't get die spending all your time getting coins.

World 8: Castle of Koopa/Dark Land

Bowser's World!
This world is in four parts, which are pasted together above.
Lots of mini-boss type levels. And the Angry Sun comes back for fun!

World 9: The Warp Zone
I guess every world doesn't end in "land"
Yep, The Warp Zone is World 9, it says so at the bottom of the screen.
I think its quite cool how they made it World 9, instead of World 0, or not a World at all.
You can Warp to this world by using one of the 3 whistles which are available in the game.
The Warp Zone is a classic feature of SMB3, allowing you to quickly travel to different worlds.

The water and land colour of The Warp Zone is the same as World 3 . . .I wonder if
they're geographically nearby?