OKR stands for Objectives and Key Results. It's a goal management framework that helps companies implement the strategy.
Andy Grove invented OKRs when he was the CEO of Intel in 1970th. He was inspired by the Peter Drucker's approach MBO (Management by Objectives). John Doerr worked at Intel and later became an advisor to Google, and encouraged Larry Page and Sergey Brin to adopt OKRs. Which they successfully did during the first year. It supported Google's growth from 40 employees to 100,000+.
Inspired by Google's example, the OKR methodology spread to other Silicon Valley companies.
Some of the companies that use OKRs include LinkedIn, Airbnb, Spotify, Dropbox, Amazon, Twitter, Booking. But it's not only for tech startups. OKRs are widely used in other industries, for example, Dun and Bradstreet, OpenX, Adept Media, etc.