A strag is someone who is not a hitchhiker and generally used to refer to someone on board a ship. It is said that if a hitchhiker with a towel approaches a strag, the strag will assume that the towel-carrying person will also be "in possession of a toothbrush, face flannel, soap, tin of biscuits, flask, compass, map, ball of string, gnat spray, wet weather gear, space suit etc., etc." The strag will then be happy to lend any of these objects to the hitchhiker, thinking that they have lost them, making them a very useful acquaintance.
A strag is likely to be impressed when faced with a hitchhiker who has seemingly hitched the "length and breadth" of the Galaxy, struggled with uncountable odds, and still knows where his towel is. The Guide's entry on towels explains that a strag will see a hitchhiker with a towel and think that he is "a man to be reckoned with."