It's Valve's level editor for the source engine, which Portal 2 runs on. This editor is more advanced than the Portal 2 ingame editor and it's also the editor they used to make the levels of the actual game.

To create maps with Hammer, you have to download the Portal 2 Authoring Tools.
You can find it by going to your Library, then make sure Tools is checked in the dropdown menu above the search bar, then search for Portal 2 Authoing Tools - Beta and install it.
After installing that, you can open it and launch hammer from there by double-clicking "Hammer World Editor".

Here are some great resources to get started with Hammer and Portal 2 mapping:

Valve developer community wiki:
Valve Developer Community: Level Design
You'll find everything there. This is your go-to page for any documentation needs.

Valve developer wiki page just for portal 2:
Valve Developer Community: Portal 2 Level Design
Some tips and tricks about Portal 2 level design

General Hammer editor tutorials (youtube playlist):
TopHATTWaffle's hammer editor youtube series

Portal 2 mapping tutorials:
Portal 2 hammer tutorials youtube playlist
In these videos you can see how to create specific Portal 2 test elements in hammer.

Portal 2 mapping community
Thinking with portals Community[www.thinking.withportals.com]
This is a forum with lots of very talented people that definitely know their stuff! You can ask anything and find answers to almost anything portal 2 mapping related in their forum.[forums.thinking.withportals.com]
There are also lots of cool maps to download, mapping contests and such!

p0rtalmaster's Hammer Guide Series (19 parts):
p0rtalmaster's steam guides • Link to Part 00
These are some helpful guides for hammer and portal 2 mapping