Does the type of yarn affect the quality of the towel?

Yes. The yarns used to make towels can vary a lot. The way the yarn is made affects the final quality - combed yarns are smoother than uncombed yarns, whereas yarns that are open-ended and have not been combed will feel less smooth.

The fibre used to create the yarn will affect the towel's quality; yarns made with longer fibres, such as from Egyptian cotton or Supima create a towel that's softer, more absorbent and more durable. Yarn quality will also affect factors such as shedding - combed yarns have had most of the loose strands removed already so will shed less and last longer.