An opposed skill roll occurs when one skill is actively resisted by another. For example, a thief attempts to sneak past a wily palace guard who, being vigilant is on the look-out for potential crooks. (pg 34)(This is a confused concept in RuneQuest because combat rolls aren't exactly considered opposed tests, which is a little discombobulating because surely combat tests are "actively resisted by another.")
You want to beat someone else at something. The defender rolls defensively and you need to meet or beat that roll offensively. (pg 9)Opposed tests don't change your odds of success. However, some tasks that you could never achieve with a single roll may be achievable with an opposed test as it opens out a larger range of results. The inverse is also true, you can fail when you normally wouldn't.
I don't know where the idea for opposed tests came from, but they're a wacky idea. One of the main issues is figuring out, philosophically, what is and is not an opposed test. In RuneQuest, sneaking past an alert guard is an opposed roll, but trying to cut her throat whilst she attempts the same to you, is not, technically. This isn't solely an issue with RuneQuest, most games seem to struggle with the concept.
Opposed tests are usually reserved for resolving a conflict of one sentient being against another. Why is that? If one wants to cross a dangerous suspension bridge, one isn't allowed to roll an opposed test against the designers/builders of the bridge. However, if one of those builders were shaking the bridge from the other end, you might be allowed an opposed test. That seems quite odd.
I think that the only logical use of an opposed tests is to use them when you want, for whatever you want and just because they are fun. Playing with opposed tests makes it feel like there is a real conflict going on. And you can stunningly succeed or fail, so that has to be fun, surely. Of course, if a game never used opposed tests, it wouldn't be any less of a game and it would definitely speed the game up a little too.