Rift is a virtual reality head mounted display developed by Facebook owned VR startup, Oculus. The headset is sometimes referred to as The Oculus, or The Rift but the proper name is simply, Rift.

Rift is the brainchild of Palmer Luckey who was 19 at the time that it was invented. With the help of John Carmack, Brendan Iribe, Michael Antonov, Jack McCauley, Nate Mitchell and Andrew Scott Reisse, he formed Oculus and had on of the most successful Kickstarter campaigns in the history of the crowdfunding site.

Rift is the first consumer headset in a line of headsets from Oculus including prototypes, some of which were publicly displayed, and some not, as well as two publicly available development kits.

Rift iterations: Duct Tape, DK1, HD Prototype, Crystal Cove, DK2, Crescent Bay, CV1; Many others that were never publicly shown
The Rift headset has 2 OLED displays at a resolution of 1080×1200 per eye, 90Hz global refresh, and low persistence. It has a rougly 110° field of view and comes with removable integrated headphones that provide 3D spatial audio.
Rift requires a powerful PC to run. The minimum recommended specs are:

Video Card: NVIDIA GTX 970 / AMD R9 290 equivalent or greater
CPU: Intel i5-4590 equivalent or greater
Memory: 8GB+ RAM
Video Output: Compatible HDMI 1.3 video output
USB Ports: 2x USB 3.0 ports plus 1x USB 2.0 port
OS: Windows 7 SP1 64 bit or newer
Depending on the parts you choose if you have to buy the computer and the Rift together you will spend around $1200 – $1500 on the PC.