If the judges in question are those in the European Court of Human Rights (they often are), then this has nothing to do with the European Union at all. I’ve written separately about this in more detail.
But the European Union does also have a court, the European Court of Justice, whose role is to adjudicate when there is disagreement about the meaning of EU law. One judge is appointed by each member country (not by an EU institution like Parliament or the Commission).
Without a common court to settle disagreements, each country could wriggle out of mutual commitments and agreements made. Remember how France tried to maintain a ban on British beef, even after it was declared safe following the “mad cow disease” crisis? This was overturned in the court as it ran contrary to the rules we’d all agreed. (By contrast, the USA refused to accept beef from Europe right up to 2015!)
As a past (British) president of the court said, the court doesn’t make political decisions, “but it does sometimes have to remind politicians of what they have agreed”!