The sizes of the hooks or needles listed in a pattern indicate the size used by the designer to achieve the listed gauge and to complete the item shown. Gauge is the number of stitches and rows worked in a piece fabric of a certain size. The hook or needle size helps determine the gauge and the gauge determines the size and drape of the fabric. Different knitters and crocheters, even when they use the exact same size hook, yarn, and pattern stitch, will often create fabric of different gauge. Accordingly, you may need to use different size hooks or needles to achieve the same results as the designer. Begin with the listed size, but check your results and be willing and prepared to change to a different size (see Gauge section below for more details).
Hooks and needles of different types may also be indicated. Knitting needles come in straights of different lengths, circulars of different lengths, and double-pointed. Crochet hooks can be standard, Tunisian, or double-ended. Be sure that you have (or are willing to acquire) the skill needed to use specific hooks and needles, especially double pointed knitting needles or Tunisian or double-ended crochet hooks.
The hook and needle sizes listed may or may not be the same as the recommended size listed on the yarn ball band. The recommended size listed on a ball band is a size needed for a fabric of average drape (or firmness) made from the most basic of pattern stitches (single crochet or Stockinette st). A specific project is likely to warrant a different drape and the use of pattern stitches other than the basics, thus needing a different size hook or needles.