I now know that the selvedge is the self-finished edges of fabric which keep the fabric from unraveling or fraying. It is also where the printing marks, company name and now the company's website are printed, which is sometimes helpful to know, especially when you've run out of that fabric but haven't finished the quilt yet. It has been customary in the past to cut off and discard the selvedge edge, although lately there's been a movement to use these edge pieces.
Above is a quilted postcard that I made using selvedges. Below is a chicken that I purchased from Etsy seller With Hugs and Stitches. She also makes whales using selvedge fabric.
The project that got me interested in selvedges was a selvedge dress made by Jodie Carleton. There are more photos of this dress on her blog Ric Rac. I'm not much of a girly-girl and I suspect that the dress might be a little heavy but it looks like it would be so fun to wear it!
There's even a whole blog just about selvedge projects, aptly called Selvedge Blog by Karen Griska. She's collected photos of selvedge quilts, purses, furniture, a lamp and even an umbrella. If you want to make a selvedge project but don't want to wait until you have that many selvedges, you can sometimes purchase selvedges from other sewers!