"EE" is a width designation in both men's and women's shoe sizes. For men's shoes an "EE" designation means wide; in women's shoes it means extra wide.
Shoes come in many different widths in addition to the standard length size. These different widths accommodate people with wider or narrower feet than the standard width. Widths use letters as a scale instead of numbers; as the widths increase, so do the letters. On the narrow end of the spectrum, more A's means a narrower shoe, while on the wide end, more E's means a wider shoe. Available widths vary depending on manufacturer and style.