Bobbin threads are a specialist thread for embroidery stitch-outs. Often, but not exclusively, they are black or white. Just like all threads, they come in various fibres, weights and qualities. A finer bobbin thread will create less bulk on the back of your work, which makes more room for the top thread and the needle to position stitches accurately.
Bobbin thread needs to run at a tighter tension to pull the embroidery thread to the back of the work, creating a shorter length of thread on the back of the stitch. No bobbin thread should appear on the surface of the embroidery, and your machine will probably have a setting or a 'higher tension' bobbin case specifically for digitised embroidery.