A per year excess means you pay the excess once in each policy year, regardless of how many different covered conditions you claim for.
With a per year excess structure, you pay the excess amount once at the start of the policy year, and after that the insurer covers its share of any further claims for the rest of that year, up to the policy limits.
For a pet who has a difficult year with multiple unrelated health issues, this can work out significantly cheaper than a per condition excess, because you're only contributing that fixed amount once no matter how many claims you make.
Where it gets more complicated is with ongoing conditions across multiple years. If your pet has a long-term condition that needs treatment every year, a per year excess means you're paying the excess again at the start of each new policy year for the same condition. A per condition excess might mean you only paid it once when the condition was first diagnosed.
So in a simple sense: per year excess tends to favour pets with multiple different issues in a single year. Per condition excess tends to favour pets with one ongoing long-term condition that runs across several years. Though in reality most people don't know in advance which category their pet will fall into.
"Per year excess tends to favour pets with multiple different issues in one year. Per condition excess can work out cheaper for one ongoing long-term problem."
This is one of those details that gets buried in the policy wording and doesn't always get explained clearly on comparison sites. If you're not sure which type your policy has, its a policy detail to check before you need to claim rather than after.