If you don't know, you won't know that a warrant is a contract that gives the holder the right, but not the obligation, to purchase additional units at a fixed price. These contracts typically, but not necessarily, have an expiration date. The holder of the warrant can exercise the warrant when the price of the token exceeds the fixed price set in the warrant, then immediately sell the token and pocket the delta.

The reason ICO contributors should do this is because it creates an incentive for the people running the project to build value such that the price of the token rises to the point that warrants are exercised and they get paid. The team gets paid only when they reach certain milestones as measured by the price of the token. It aligns the economic interests of the investors with the economic interests of the developers much more so than simply handing the developers a huge sum of cash before they have delivered any value.