FurMark is an OpenGL benchmark that stress-tests your graphics card with fur rendering.
At its simplest, you can use the program as a speed test to confirm that your graphics card is delivering the performance you'd expect. Just launch the program, choose the Benchmarking option, and click Go. Once the test is complete you'll see your scores, and can then upload and compare them with others. (Or simply point your browser at http://www.ozone3d.net/benchmarks/furmark_scores.php, where the last 10 uploaded scores are always displayed.)
If you've overclocked your graphics card, though, you can also use FurMark to confirm that it's stable. Choose the Stability test, click Go, and this time the program will carry out a far more intensive benchmark: if your system survives this, then the overclock is solid and shouldn't cause you any problems with other applications.
Of course it's possible your overclock might not survive, and that could be very bad news. Your display may go completely blank until you reboot, for instance. But if the stress test has generated too much heat, then it may cause physical damage to the card: unlikely, but it could happen.
Always save your work before you run FurMark, then. And if you're running the Stability test, check the option to log your GPU temperature. This will let you monitor the effects of any overheating, and you can close the test down if the card is getting too hot.
Version 1.15.1 changes:
+ added 4k resolutions: 3840x2160, 7680x2160 and 11520x2160.
* fixed the display of benchmark percent in the progress bar.
! updated Radeon HD 7850 / R7 265 GPU database entry.