A warrant is an agreement giving the holder the right to buy (or sell) a certain number of shares of a company.
Warrants are often requested or granted when a company engages in a loan from private investors - it will give the lenders the opportunity to buy and own shares in the company if its stock appreciates or if the opportunity seems attractive.
If the company fails to grow and deliver, the warrants can simply go unused with no financial impact for the holder. Like options, there are warrants that confer the option to buy shares (call warrants) and those that allow the holder to sell (put warrants).
Traditional warrants are linked to bonds, also known as warrant-linked bonds. These types of bonds generally are designed to attract more investors, since they have greater upside potential but limit downside risk.