A person born during the temporary peak in the birth-rate that occurred in several countries following WWII, notably the USA and the UK.
A 'baby boom' is any temporary increase in the birth-rate and that term was in use some time before WWII. A 'baby boom' was reported in various newspapers in England in the 1920s; for example, this piece, reprinted in The Coshocton Tribune, April 1920:
There is a 'baby boom' in London. Births during the first six months of this year have broken all records.
'The Baby Boom' - as opposed to 'a baby boom', refers to the increase in population in the countries that were victorious in WWII. The period is generally regarded as beginning in 1946 and ending in the mid-1960s.
There are citations of the term being used in the USA prior to or very early in WWII. At first sight these tend to contradict the view that it referred to the increase in the birth-rate due to the war. Logic would suggest that any baby boom couldn't begin until at least nine months after war had become inevitable and the USA had declared itself neutral in 1939. Those 1939/40 references to a 'baby boom' don't relate to a boom in the number of babies though, but to a small boom in the stock market. This growth in the economy was caused by an upsurge in manufacturing resulting from increased trade with Europe due to WWII. This 'baby boom' was widely reported in the US press in late 1939 and early 1940; for example, this item from The Syracuse Herald-Journal, April 1940:
"Stocks with a war flavor bounded up to more than 4 points in today's early market, in the fastest sprint since the 'baby boom' of last fall, but the majority stumbled badly in the latter part of the proceedings."
The 'boom' in babies didn't wait until servicemen returned from the war, as is popularly supposed. There was a temporary increase in the birth-rate when the US effectively entered the war in 1941, as reported by The Galveston Daily News in December, 1941 - "Baby Boom Increases Population of U.S.". There was some speculation about the cause of this at the time and some commentators put it down to men trying to avoid the draft by becoming parents - an unsuccessful ploy if true, as many new fathers were drafted into the forces in WWII.
Babies no longer... In 2016 many well-known baby boomers died.
The term 'baby boomer' was coined in the USA, clearly with reference to the already widely known 'baby boom'. This wasn't for some years after WWII and the earliest citation I've found is surprisingly late - a piece in The Bennington Banner from December 1977:
"I grew up in suburban Massachusetts, a postwar baby boomer not used to seeing empty seats in classrooms or enough textbooks to go around."
The term 'baby boomer' was initially used simply with reference to the peaks in birth-rate in the USA and UK. Over time, the connotations of the term have widened. The major economic, social and demographic changes that have been lived through by the postwar generations in the Western world have given the 'baby boomers' a unique position. They are healthier and wealthier than previous generations and can look forward to an active old-age that was denied previous generations, and also probably future ones as western economies struggle to maintain pension provision. The 'boomers' also developed rebellious, anti-establishment attitudes which have been carried on into older age, which is in contrast with a previous more deferential society and late 20th century apathy.
The 'baby boom' has led on to other expressions - 'baby bust' and 'echo boom'. These refer respectively to the period of relative low birth-rate in the 1950s which resulted in low school enrolments in the 1960s and the high birth-rates in the 1970s, when the original baby boomers had their children. These terms were both referred to in an article in The Newark Advocate, August 1975:
"Newark was not the only school district caught by surprise by the 'baby bust.' Population experts expected the postwar baby boom children, now grown, to produce an echo boom in the 1970s."
See other phrases that were coined in the USA.