I agree that paper piecing (aka foundation piecing) is one of those love it or hate it things however I'm in the rare "it's better for certain stuff" category. I wouldn't even attempt a New York Beauty or Mariners Compass type block without paper piecing. Some people also call it flip & sew because you line your fabric up on one side of the paper and then you flip the paper over where your printed lines are and sew o the lines. You'll get even more confused when you read about freezer paper foundation piecing where you don't sew through the paper, muslin foundation or QuiltSmart foundation where the pattern is printed on muslin or interfacing and is not removed--crazy quilting is often done on a muslin foundation, and English Paper Piecing which is fabric wrapped or basted around plastic or paper shapes and then the shapes are whip stitched together by hand--think Grandmother's Flower Garden or Hexagon quilts but there are many different English Paper Piecing designs.
Many people can't seem to sew a pattern with triangles to save their soul so they are in the "Love it" category. Other folks would rather sell their soul than have to pull all the paper back off or just can't get the hang of "flip & sew" so they are in the "Hate it" category.
A very good pattern to practice on is Square in a Square or a simple Log Cabin/Courthouse Steps type block where you are sewing basically the same shape over and over. That teaches you the flip & sew method without having to line up odd-ball angles. I screw up the weird shapes repeatedly even after paper piecing for the past 7 years.
If you've never sewn before or are working on an unfamiliar machine; paper piecing is good for teaching you to sew in a straight line.
My avatar was paper-pieced and I had only been quilting for about a year when I made it. The first thing I did as a newby quilter was join a swap and then chose blocks that were way beyond my skill level so paper piecing was the only way I could accomplish what I had stupidly promised to deliver--Stars. The second over my head swap was paper pieced butterflies. That mistake taught me how to design my own paper pieced patterns so I could deliver what I promised.