What is Blender?
Blender is a free and open source 3D animation suite. It supports the entirety of the 3D pipeline—modeling, rigging, animation, simulation, rendering, compositing and motion tracking, even video editing and game creation. Advanced users employ Blender’s API for Python scripting to customize the application and write specialized tools; often these are included in Blender’s future releases. Blender is well suited to individuals and small studios who benefit from its unified pipeline and responsive development process. Examples from many Blender-based projects are available in the showcase.1
Even though at the beginning Blender was often criticised as not being up to industry standards (especially on it's interface), but since Blender 2.5 was released in 2011 with a completely reworked user interface it can easily sit beside the major players such as Maya, 3ds Max etc.
It is also noted as the most all-around solution with the most extensive feature set (and keep in mind that Maya and Max are around 3500$ each, so that's another plus for Blender).
Blender has been growing in popularity even in the media industry, with more and more bigger projects opting to use it instead of the "standard" tools.
Where is Python used?
The feature that makes Blender stand out the most is it's Python API, which allows anyone to easily create scripts/addons, many of which are integrated into later releases. Since I'm totally clueless about anything design-related, I can't tell you which ones are good and useful, so I guess Google is your friend here :).
With Python and the included
bge module you can even use Blender to create
Examples of videos
Since Blender is primarily an animation suite, you can find many great Blender animations on the web.
Every 1-2 years the Blender Foundation announces a new creative project to help drive Blender and it's innovation forward. Below you can find it's latest project, the Tears of Steel. Ignore the (imo) so-so acting and (again, imo) not the best story and focus on the animations ;).
PS: It even comes in a Chinese version, using their own actors but re-using the animations.
Examples of games
While there are quite some games made in Blender, not many of them achieved global recognition. Below is a trailer from Dead Cyborg, a Steam Greenlit free donation based oldskool sci-fi adventure game. I've read good things about it, so I'll be sure to check it out when I get the chance.
I've also found Mattline1's blog and videos really nice - lots of nicely implemented good ideas, it seems he is very talented. I found his Sphere shooter especially interesting, and I believe it nicely shows off that Blender can actually be used for games too.