Warrants represent an option to purchase a certain number of shares (common or preferred) at a future date at a fixed price, which can be the price of the current round of financing or set at a premium to the current price per share.
Warrants tend to be used in earlier-stage deals to compensate an investor helping you to raise startup financing (in lieu of or in addition to cash). Warrants can also be used in later-stage deals or strategic rounds to provide upside potential value to investors to encourage participation in a round of financing.
Unlike stock options, warrants tend to provide an option to purchase the most recent class of shares (rather than common shares). Warrants can also be issued to third parties while stock options are limited to employees, directors, consultants and advisors engaged in the business.