A user-generated endorsement of a person, company, product or service on the LinkedIn network.
LinkedIn Recommendations are a great way for others to get a sense of your professional expertise.
You can ask others to endorse you. Once they do so, then you'll have the opportunity to review them. And likewise, you can go to colleagues profiles and recommend them.
Three recommendations are required to have a 100% complete profile.
This video from LinkedIn shows a quick overview and there are more LinkedIn Tips here.