What does it mean "good honours degree" or "Upper Second Class (2:1) UK honours degree"?
Does it depends on average score?

See our PhDs Explained section for links and information relating to qualifications and equivalent grades.

In the UK (and many other countries) degrees are graded as follows:
1st class honours
2nd class honours grade 1(2:1)
2nd class honours grade 2(2:2)
3rd class honours
Pass
It usually depends on the score you get in your final year exams, along with any final year projects. Results from earlier years are not normally counted in the score. If you come from a different educational system, they usually take that into account.