They were identification aids for Allied pilots and gunners. Friendly fire was a persistent risk for aircraft, positive recognition being difficult in the heat of battle; the first Fighter Command losses of the war were in the "Battle of Barking Creek" during which two Hurricanes were shot down by Spitfires and the introduction of further combatants and types of aircraft only made the situation more confusing. An early use of black and white stripes was on the wings of Hawker Typhoons in 1942 as they were frequently mistaken for the Focke-Wulf 190. Frank Zeigler, intelligence officer of 609 Squadron, wrote in the RAF Flying Review about the results of the confusion: "Once a gunnery officer, whom I had just 'blitzed' on the phone, actually called back with the request: 'Could you ask your pilots tactfully - very tactfully - did we get anywhere near them?' Sometimes they did. Roy Payne, wading ashore after being hit and crash-landing in shallow water, really lost his temper when the coastguards addressed him in German." See also an Imperial War Museum photograph: "A Hawker Typhoon Mk 1B in fighter pen at North West corner of RAF Duxford (...) The black and white stripes painted on the underside of the wings - sometimes referred to as 'Dieppe stripes'- were actually introduced following the failed Dieppe Raid of 19 August 1942. Originally only black stripes were painted on but white stripes were added by December 1942 for greater recognition by other RAF aircraft who had mistaken the Typhoon for the German Focke Wulf 190."

During the 1943 invasion of Sicily C-47 transports suffered particularly badly from friendly anti-aircraft fire, 23 of 144 being shot down on 11th July. As a result during the planning of Operation Overlord a memorandum on "Distinctive Marking - Aircraft" was written:

"1 OBJECT
The object of this memorandum is to prescribe the distinctive markings which will be applied to US and BRITISH aircraft in order to make them more easily identified as friendly by ground and naval forces and by other friendly aircraft.

(...)

4 DISTINCTIVE MARKINGS
(a) Single engine aircraft. (1) Upper and lower wing surfaces of aircraft listed in paragraph 2g above, will be painted with five white and black stripes, each eighteen inches wide, parallel to the longitudinal axis of the airplane, arranged in order from center outward; white, black, white, black, white. Stripes will end six inches inboard of the national markings. (2) Fuselages will be painted with five parallel white and black stripes, each eighteen inches wide, completely around the fuselage, with the outside edge of the rearmost band eighteen inches from the leading edge of the tailplane."

(etc)

The order was issued on June 4th, leading to rather frantic painting for the squadrons involved, and can be considered a success, there being no large-scale repeat of the Sicily incident.

Further reading:
US Army Air Forces Aircraft Markings and Camouflage 1941-1947, Robert D. Archer
"Fratricide - An Overview of Friendly Fire Incidents in the 20th Century", RAF Historical Society Journal No. 34, Wg Cdr C G 'Jeff' Jefford