When paper piecing, you print the block pattern directly onto paper and then have to tear the paper off when your blocks are done. It is much easier to remove the paper if you use a size 14 sewing machine needle and a smaller stitch lengh (like 2.0).
When you foundation piece, you print the block pattern onto a foundation instead of paper. You can use muslin (backed by freezer paper so it will feed through your printer), or you can buy foundation sheets made by June Taylor from JoAnns. They are very lightweight and similar to dryer sheets -- and I always use a coupon of course! I have used both methods and very much prefer the foundation sheets. Besides mariner's compass, this method is also great for the Pineapple pattern!