The Concise Oxford Dictionary defines 'honours' as, "special distinction for proficiency at examination, course of degree studies more specialized than for ordinary pass".
A few institutions offer differing courses of study for, say, BA and BA(Hons), where the 'Hons' course involves a greater depth of study. i.e. the second of those two dictionary definitions applies.
For most university courses, however, it is the first definition which applies. i.e. students study a common course. Those that do well in the examinations are awarded an 'honours' degree, those who 'scrape through' are awarded a 'pass' degree. In most universities, honours are divided into 4 divisions (1st Class, 2.1, 2.2 and 3rd Class). Anyone achieving one of those levels (even a humble '3rd', like mine!), is entitled to add '(Hons)' after the abbreviation for their degree. A student who only achieves a 'pass' is not entitled to do so.
Chris
Incidentally, did you realize that a degree is actually a class of 'membership' of a university? There are some religious groups which prohibit their members from holding membership of any other organization. When graduates join these religious groups, they're obliged to contact the university and ask that their degree be withdrawn in order to comply with the rules of their religion.