A batman (or batwoman) is a soldier or airman assigned to a commissioned officer as a personal servant. A batman's duties often include: acting as a "runner" to convey orders from the officer to subordinates; maintaining the officer's uniform and personal equipment as a valet; driving the officer's vehicle, sometimes under combat conditions; acting as the officer's bodyguard in combat; other miscellaneous tasks the officer does not have time or inclination to do. The action of serving as a batman was referred to as "batting". In armies where officers typically came from the upper class, it was not unusual for a former batman to follow the officer into later civilian life as a domestic servant.

OK, so just who was this batman? Wikipedia says:

John O'Neill was a professional musician born in County Durham, England to Irish parents. He was famous for his whistling abilities and was also an accomplished trumpeter.He is widely believed to have had a hit single with I Was Kaiser Bill's Batman credited as Whistling Jack Smith (a play on "Whispering" Jack Smith). However the exact nature of who Jack Smith was is unsure; certainly in TV appearances an actor lip-synced whistling to a backing track, and some sources attribute the single to British Decca/Deram producer Noel Walker, as producer and performing artist.

But wait! What about "Kaiser Bill?" Dustbury.com says:

Forget stately Wayne Manor. The real question here is why Kaiser Wilhelm II, emperor of Germany and king of Prussia, would have needed a small-b batman (a British soldier assigned duty as servant to an officer) in the first place. And when that's settled, we can work on the question of "Who was Whistling Jack Smith?" The name is a send-up of singer Whispering Jack Smith, soft-spoken because of an injury sustained in World War I; many of the noises are made by the Mike Sammes Singers, well-known in Britain but in the USA perhaps best-known for being the parents of the kids chanting on John Lennon's "I Am The Walrus", and the leader of all the whistlers was recording producer Noel Walker. The tune was orignally titled "Too Much Birdseed" (!) and was concocted by Roger Cook and Roger Greenaway, previously of the Kestrels; their song "You've Got Your Troubles" (also produced by Walker) became a major hit for the Fortunes, and as "David and Jonathan" they did a successful remake of the Beatles' "Michelle" in 1966. Everyone at Decca, owner of the Deram label, seemed surprised that this little ditty became a hit, and in an effort to keep the hype going, the label designated singer Coby Wells, real name Billy Moeller (brother of Tommy Moeller of Unit Four Plus Two), already signed to Decca, as the "official" Whistling Jack Smith for touring purposes. Greenaway and Cook would go on to write many other songs; perhaps their biggest hit was "Long Cool Woman In A Black Dress", the Hollies' crunchy Creedence pastiche. Billed as an instrumental, "...Batman" actually contains one word, uttered by Noel Walker: curiously, it's "Hey!" on the 45 and "Oy!" in the stereo mix.

There. I hope that's clear now.

The menacing stalking sound of "Rumble" (and its title) led to a ban on several radio stations, a rare feat for a song with no lyrics, on the grounds that it glorified juvenile delinquency. Nevertheless it became a huge hit, not only in the United States, but also Great Britain, where it has been cited as an influence on The Kinks and The Who, and Jimmy Page among others. Jimmy Page cites the song in the Davis Guggenheim documentary "It Might Get Loud" and proceeds to play air guitar to the song in the movie. Pete Townshend stated in unpublished liner notes for the 1970 comeback album, "He is the king; if it hadn't been for Link Wray and 'Rumble,' I would have never picked up a guitar." In other liner notes in 1974, Townshend said, of "Rumble": "I remember being made very uneasy the first time I heard it, and yet excited by the savage guitar sounds."