A penny warrant is a form of warrant where the exercise price is set at a nominal price, often $0.01. This means the warrant holder can purchase shares at a penny per share.
Penny warrants may be used as sweeteners in startup financings. For example, an existing investor who pays full price for shares in a financing may also be given a penny warrant as a way to sweeten the deal for the investor. That way, if the startup does well and the share value increases, the investor will be able to own more of the company for quite literally pennies.