The percentage of an eligible claim you still pay yourself, before or after your excess is deducted (depending on your plan).
Usually, after your excess is deducted, the co-payment is the percentage of the remaining eligible amount that you still pay. The insurer pays the rest. A 20% co-payment means the insurer pays 80% of the bill above your excess, and you pay the other 20%. A nil co-payment means the insurer pays 100% of the eligible amount above your excess.
A handful of insurers advertise a low “headline” co-payment rate but apply a materially higher rate in specific, common scenarios. For example, a specialist referral, a chronic or ongoing condition, or once a pet reaches a certain age. Those override co-payments are worth checking directly, since the headline number isn't always the one you'll actually see on a real claim.