Meaning of 'Set auto-complete' in ADO

When performing a PR from a child branch to main/master in ADO, what does the button Set auto-complete mean?

That means that the PR will automatically complete (merge and close) when all its requirements are met. For example, if you have a policy that requires one of a group of code reviewers to approve the PR and a verification build to complete successfully, as soon as any of the reviewers approve the PR and the verification build completes successfully, then the PR will automatically complete without anyone having to click Complete. When you set up the auto-complete you have the option to set things like deleting the source branch (and a couple of others) and it will take those actions when completing.

Please make sure you tell your devs to use the auto-complete feature when they set the PR especially deleting the original branch. Dont keep branches you dont need after they have been merged.
The only other ability ti choose is what type of merge you want them to use as you can limit that in the branch policy. Though this is a more advanced topic.