The only context you should ever provide, in this situation, is the context that a user would arrive with. Anything else is going to confound your results. Many times, if your testers are properly screened, you won't require any explanation at all.
If you have a client who is providing a new testing mechanism for people with diabetes, and you sit a group of Type-I and Type-II diabetics down at a screen to make sure they understand the landing page + call to action, you probably don't need to give them any context. If they miss the boat, you've made a mistake.
On the other hand, if you're working with a college website and you want to make sure that students are able to find the new classes being added for the Fall semester, which were not offered before - well then you need to give them a bit of context. You've got college students at the school as testers, and that's good, but how much context is appropriate?
This is what several types of user testing are designed to do. You literally give the tester a task:
"Find the newly added courses for your major and register for one of them" (your context is now built in)
- Reverse Card Sort: Locate it in a tree
- Click testing: Locate the first-click correctly on a screenshot
- Beta testing: Observe the person as they attempt to do it on a live site
Note, I didn't need to tell them what the site was about, because they already know, having been properly screened. I might need to tell them what I want them to try to accomplish, especially on a more complex site.
As a general rule though, I want to keep my explanation as simple as possible, in order to avoid polluting results and causing Type-1 or Type-2 errors.