A counter-model, also called a counterplan in some formats, is an alternative policy the Opposition proposes instead of simply rejecting the Proposition's plan. Rather than arguing 'do not do X,' the Opposition says 'instead of X, we should do Y, because Y solves the same problem better.'
Why Use a Counter-Model
A counter-model shifts the burden of the round. Instead of defending the status quo - which the Proposition has just criticized - the Opposition offers a different forward-looking alternative. This lets them concede that the status quo is flawed (sometimes unavoidable) while still opposing the specific Proposition plan.
When Counter-Models Work
Counter-models work best when the Opposition has a genuinely better alternative that solves the same underlying problem. They work poorly when the alternative is unrelated to the motion or when it fails to address the harm the Proposition identified. Judges usually evaluate counter-models by comparing them directly against the Proposition plan rather than against the status quo.