Twill is a basic weave structure, distinct from the simpler plain weave used in fabrics like poplin. Instead of the weft thread alternating over and under a single warp thread each time, in twill it passes over one or more warp threads and then under two or more, shifting slightly with each pass. Repeated across the whole fabric, this creates the diagonal rib line that twill is known for.
Denim is, by definition, a cotton twill fabric, and the twill structure is part of what gives it both its diagonal texture and its drape, which is generally softer and more flexible than a plain weave fabric of similar weight. The angle and tightness of the twill also affects how the fabric fades, since the raised parts of the weave wear first.
Twill direction is described as right hand or left hand depending on which way the diagonal line runs, which is a detail some denim enthusiasts pay close attention to. See right-hand twill and left-hand twill for how the two differ, and our denim guide for the bigger picture on fabric structure.