Paper piecing is where you sew the fabric directly to a paper pattern, and then tear it off when the block is completed. It is used for blocks that have many small pieces and where there are sharp points that are difficult to piece the traditional way. Carol Doak is the queen of paper piecing and she has tons of books on the subject, which will illustrate it far better than I can tell you about it. Check out her website at
www.caroldoak.com . For me, paper piecing is counterintuitive since you sew the bits of fabric to the back of the printed pattern and I always get it mixed up somewhere along the line when I first start a quilt. But then muscle memory takes over and I get it...With some patterns, like the Storm at Sea, it makes it so much easier to get the blocks accurately put together.
And then there is English paper piecing, which is a whole different story..... hopefully someone here will have done it and can explain that to you because it just looks too tedious to me!!!
Good luck!!