It's a word that comes up a lot, but what is it? It's not an ideological package of its own. My own expression of it would be something like Blairism and "triangulation": explicitly picking popular points from left and right and trying to find a fusion to appeal to moderate voters from both poles. So for Blairism the compromise was tax rises but never touching income tax; leaving the welfare system fairly generous, but charging students more; retaining public health and education, but leaving more of the implementation to PFI schemes to keep it off the public balance sheet.
Centrism seems to be associated with "liberal" ideas of free trade and free movement of people, as well as a technocratic process of cost-benefit analysis and consensus decision making. This makes the EU the ultimate centrist body. The ne plus ultra of centrism is reducing everything to a cost-benefit analysis.
Centrism is also associated with the post-Berlin Wall consensus and the "end of history" view.
To me the beginning of the end of centrism was the first plane strike on the World Trade Centre. The consequent war was widely supported by the political class and widely opposed by a section of the public - but crucially the discussion of why and how it was being done was inadequate and informed by misleading reports on Iraq "weapons of mass destruction". The absurd cost of the war was the first nail in the coffin of cost-benefit politics.
The second dent in centrist consensus was the end of a long-running housing and mortgage bubble. This took out a number of old banks and forced the bailout of many more, at taxpayer expense. The vast majority of the money was eventually recovered - you will see huge figures quoted, but they were loans not gifts. But the fact that huge amounts of money could be committed to the stability of the financial class while ordinary people suffered or were bankrupted has left a big mark on public trust. Especially the treatment of Greece and Ireland by the EU.
The war in Iraq and Afghanistan spread throughout the Arab world; Syria and Libya have collapsed resulting in people fleeing in huge numbers. Many of these people have been coming to Europe. The west is faced with the choice of allowing a lot of Muslims to immigrate, who will require public support in the short to medium term, versus letting them die (or, as some far right commentators have suggested, actively murdering them).
The internet has greatly contributed to the collapse of boring centrist journalism and its replacement with sensationalism, clickbait, and incitement to racism. Although plenty of the papers were quite capable of printing trash on their own initiative. The press likes conflict, which centrism does not provide. UKIP, for example, have been given far more media coverage than one would expect for a party which wins so few seats at Westminster elections.
This is right at the bottom, because it's so overstated, but needs mentioning: a mixture of thinktanks, foreign intelligence agencies, and bored teenagers are inserting all sorts of fake news into public discussion. A number of the non-centrist parties have opaque funding.