An alternating knot diagram is a knot diagram in which the crossings alternate between "over" and "under" as you travel along the knot. An alternating knot is a knot which has an alternating diagram.
For example, the diagram for the trefoil knot 31 below is alternating, whereas the diagram for the knot 819 is not alternating.
 Lickorish, W. B. R., An introduction to knot theory. New York: Springer (1997).