The Nintendo 3DS was the follow up to the Nintendo DS. It offers two screens in a hinged form factor. The visuals are higher resolution and the top screen offers lenticular 3D effect that you don't need glasses to see. There are a number of versions of the handheld: 3DS XL was a larger version, 2DS was a hinge-less version for younger players, New 3DS offered enhanced visuals and controls and the New 2DS offers a robust hinged version.
There are a huge range of games available on the 3DS. You can purchase cartridges or buy them via the electronic store that is on the system. You can also play all of the DS game library on any of the 3DS/2DS systems.