This is a new word for some, mostly because it has had a life only in niche texts, but it has in fact been around since the early 1900s. Initially it was just a fancy way of saying precariousness, modelled on the French precarité. In the 1950s it took on a new life as a specialist word. It is defined in Macquarie Dictionary as:
noun a state of existence characterised by precariousness, particularly in relation to jobs, income and material wellbeing, affecting one's state of mind.
This quote from the Catholic Worker of 1952 reads: Precarity is an essential element of poverty.
There is a slight distinction in use between precariousness and precarity. A situation, one’s health, a set of steps, these things can all be precarious and present a danger. These things suffer from precariousness, but a person endures precarity.
Google ngrams reveals a steep rise in frequency of use from the 1950s to 2000.
A rather more recent related word is precariat, a blend of precarious and proletariat. This seems to date to the late 1980s where it is used in inverted commas to indicate its newness. It has also had a sharp increase in frequency over the last few years, although the more frequent reference is to the left-behinds, those people whose jobs are swept away from them by global economic change.
I like both precariat and precarity but I think it will be a while before we have banners in the street denouncing them. My spellchecker agrees with me. It finds both words quite upsetting.