In debate, a link is the logical chain that connects a premise to a consequence. When you argue that a policy will lead to an impact, the link is the step-by-step explanation of how the policy actually causes that outcome. Strong arguments have clearly explained links; weak arguments leave the link implicit and assume the judge will fill it in.
Why Links Get Attacked
Attacking a link is often the most efficient rebuttal strategy. You do not need to argue that the other team's impact is wrong - you just have to show that their policy does not actually lead to the impact they claim. If the link breaks, the impact does not apply, and their entire argument collapses.
Link Chains
A link chain is when multiple links connect a policy to a distant impact. For example: policy leads to outcome A, outcome A leads to outcome B, outcome B leads to the final impact. The longer the chain, the easier it is for the opposing team to attack one link and break the whole argument. Skilled debaters keep link chains short when possible.