A covenant is a promise to either take or refrain from taking some specific action. A restrictive covenant concerns duties or restrictions upon an individual. In the business and employment context this usually refers to the non-competition and non-solicitation covenants. Employers use restrictive covenants to protect their interests and remain competitive against employees who may be looking to branch-off and use insider knowledge to gain an edge.
When the matter involves the sale of a business, the vendor would usually be expected to enter into a restrictive covenant to assure the purchaser that the former would not solicit its old clientele or open a competing business within a certain distance from the old place of business.
By having the vendor effectively make a legally binding promise that they will not compete against the purchaser or approach the clients of the purchaser – that purchaser is able to protect his business, at least for a time.