You usually have to be a student (or teacher for school purchases).
The discount is variable, and is shown on the educational Apple Store for your institution, or at your campus computer store if you have one. Often close to 10% on hardware, more on software, less on 3rd party accessories.
There are occasional hot deals, but I'm not sure if there are always refurbished options.
Click on the education store and read the details.... discounts range from 0 to 200 depending on the price and product ( higher price generally equates to a higher discount ). Generally the discounts do not apply to refurbished as they are already discounted.
Basically you have to be a student, faculty, or staff at any accredited institution for learning or can provide sufficient documentation of homeschooling status.
You have to be a student at a college or university, or faculty/staff at a K-12 or college/university. The discount varies based on the item, for cheap stuff it's generally 10%, and that's a reasonable ballpark figure for the more expensive stuff, though it can vary a fair amount. Don't know about refurbished items...
I agree with the above posters...but I would add that Apple occasionally has a different refurb. or specials under the "looking for a great deal" link. I have seen this on two separate occasions when browsing the apple.com store. So if you are an educator or student check those out to be sure there isn't a great deal that might not be available to the general public.