A warrant is the reason an argument is true - the explanation that connects a claim to a conclusion. Every real argument in debate has three parts: a claim (what you are asserting), a warrant (why it is true), and an impact (why it matters). A claim without a warrant is just an assertion, and judges consistently dismiss unwarranted claims.
Claim, Warrant, Impact
The claim-warrant-impact structure is the single most useful framework new debaters learn. Claim: 'Raising the minimum wage will reduce poverty.' Warrant: 'Because workers earning below a living wage are the primary demographic in the poverty statistic, and wage increases shift them above the threshold.' Impact: 'Reducing poverty by X percent improves health outcomes, school performance, and economic mobility for the next generation.' Without the warrant, the argument is just a slogan.
How Judges Use Warrants
Judges weigh warranted arguments higher than unwarranted ones. If one team says 'their policy will fail' with no warrant, and the other team says 'our policy will succeed because of X mechanism Y evidence Z precedent,' the judge will almost always prefer the warranted side. Rebutting a warrant also means attacking the reasoning, not just the claim.