In the UK, Australia and New Zealand, the two fingers (sometimes also two-fingered salute) is a sign whose meaning can approximately equated to the middle finger which is used in North America, Europe and probably other places. Both are a hand gesture with the palm facing inwards and fingers streched out: index and middle finger in the case of two fingers. It can be described as the opposite of the peace sign (in worldwide use) which has the same finger arrangement but the palm points outwards.
The origin of this sign remain obscure but it has been attested back in 1901 when workers were filmed outside Parkgate Iron and Steel Co. in Rotherham and one was obviously unhappy (Screenshot below).
This source points to a likely working class origin. Churchill, prime minister during World War II and upper-class, intended to introduce a V for victory hand signal. Photographs exist of him doing both what would become the peace (or victory) sign and its opposite, the two fingers. The film Darkest Hour contains a scene in which a typist of lower class origin has to alert the prime minister that his gesture with palm inwards has an established meaning and the short scene ends with confirmation that the palm facing outwards is fine. To the best of my knowledge, it is not attested whether Churchill was indeed unaware of this sign due to his upper class origins or whether he deliberately used it for its double-entendre—a double-entendre that would have been completely lost across the Channel anyway.
For a more contemporary account of the offensive nature of the two fingers, see the image below of British cyclish Mark Cavendish where he celebrated his victory by insulting his critics according to Reuters UK.