What's the meaning of the phrase 'Pip-pip'?
Pip-pip is, or rather was, colloquial greeting or word of farewell, typically used by the English upper and middle classes in the first half of the 20th century.
What's the origin of the phrase 'Pip-pip'?
The British term 'pip-pip' was first used in imitation of a high-pitched car horn. It's the kind of thing that the exuberant Mr. Toad might have exclaimed when careering around in his car in Wind In The Willows. There are several examples of the expression being used with that meaning from the late 19th century.
The meaning changed soon afterwards and began to be used as a greeting or word of farewell. The earliest example that I know of in print explains the meaning. That's in a report of a conversation between the two US authors Mark Twain and Bram Stoker while Twain was holidaying in England, printed soon afterwards in the US newspaper The Brooklyn Daily Eagle, August 1907:
When Mark Twain and T. G. [Dulaney] were strolling along London's streets, a month or so ago, they were puzzled by the alarming frequency with which the shrill "Pip-pip" and the melodious "Toot-a-loo" greeted their ears. Bram [Stoker, who was then literary agent living in London] told them that "Pip-pip" and "Toot-a-loo" were London's latest and most approved form of affectionate greeting between friends and that the salutations were derived from the sounds given forth by the bicycle bell and the automatic horn.
Not only does that neatly define the term it fairly accurately dates it. Apart from the minor misspelling of 'toodle-oo' the article reports the facts as we now know them.
There's not a great deal more to be said about 'pip-pip'. It's now a museum piece and only likely to be heard in dramatisations of Jeeves and Wooster, but it would be a shame for it to disappear completely.