http://www.diablowiki.net/Greater_riftThis is a little easier way to explain.
Or, a greater rift is a no loot, 15 minute timed way to level up legendary gems. Greater rifts are also the only way to get the legendary gems as well. The way to access a greater rift is to get greater rift stones from normal rifts (torment 6 being guaranteed).
Skills and gear is also locked in a greater rift meaning you are unable to change these and there is also a death penalty of 5 seconds per death to a max of 30 seconds.
After killing the rift guardian you get a loot drop (higher the difficulty the better) and Urshi will appear granting you access to level gems up 3 times. Gems can be leveled with at least a 60% chance of success up to the level of the rift (ie, grift level 10 can level a gem upto level 10) before the success rate drops. You can also get 100% success rate if you do a rift at least 9 levels over where you intend to level the gem to (rift level 17 for a level 5-8 gem).
Also, with this patch you can now empower the rifts for a gold amount which lets you level a gem a fourth time with Urshi if successful but starts to get expensive at later levels.
Since this is being wrote by me will just add blah blah blah and blah.