It does indeed pertain to the UK university system.
At university a three year course is usually called an honours degree. There are four possible grades: 1st (a first), 2:1 (a two-one), 2:2 (a two-two) and 3rd (a third). A first and a 2:1 are considered 'good' grades and therefore you would have 'a good honours degree', but I'm not sure about a 2:2.
You can also finish a course with a grade but without the honours. I don't really understand that though!
In the Uk university system, a degree with honours, for example batchelor of science (hons) annotated as: BSc (hons) the honours shows that a disseratiion was submitted and marked as part of the marking process. Therefore, any degree from the UK system without honours I.E. BSc - shows that a dissertation was not a requirement of the formal marking process. Previous comments are correct, a good honours degree would be a first or 2:1 but would require a dissertation in a relevant subject matter for that course, otherwise, by definition it could only be a 'good degree' So a good honours degree = achieving a 2:1 or first in a relevant degree subject, and writing a dissertation which has been incorporated into the marking process to achieve a honours degree.