The original quotation that explained the importance of towels is found in Chapter 3 of Adams' work The Hitchhiker's Guide to the Galaxy.
A towel, it says, is about the most massively useful thing an interstellar hitchhiker can have. Partly it has great practical value. You can wrap it around you for warmth as you bound across the cold moons of Jaglan Beta; you can lie on it on the brilliant marble-sanded beaches of Santraginus V, inhaling the heady sea vapours; you can sleep under it beneath the stars which shine so redly on the desert world of Kakrafoon; use it to sail a miniraft down the slow heavy River Moth; wet it for use in hand-to-hand-combat; wrap it round your head to ward off noxious fumes or avoid the gaze of the Ravenous Bugblatter Beast of Traal (such a mind-bogglingly stupid animal, it assumes that if you can't see it, it can't see you); you can wave your towel in emergencies as a distress signal, and of course dry yourself off with it if it still seems to be clean enough.
More importantly, a towel has immense psychological value. For some reason, if a strag (strag: non-hitch hiker) discovers that a hitchhiker has his towel with him, he will automatically assume that he is also 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. Furthermore, the strag will then happily lend the hitch hiker any of these or a dozen other items that the hitch hiker might accidentally have "lost." What the strag will think is that any man who can hitch the length and breadth of the galaxy, rough it, slum it, struggle against terrible odds, win through, and still knows where his towel is, is clearly a man to be reckoned with.
Hence a phrase that has passed into hitchhiking slang, as in
"Hey, you sass that hoopy Ford Prefect? There's a frood who really knows where his towel is."
/Douglas Adams, The Hitchhiker's Guide to the Galaxy/
(Sass: know, be aware of, meet, have sex with; hoopy: really together guy; frood: really amazingly together guy.)
The emphasis on towels is a reference to Hitch-hiker's Guide to Europe by Ken Welsh, which inspired Adams' fictional guidebook and also stresses the importance of towels.