Blairism is/was the mythical 'third way' - the apparent miracle of being able to hold socialist principles whilst enacting capitalist financial policy and looking out for globalised interests in the military and higher-level economy. People thought he'd actually done it back in 1997, they thought he'd invented caring capitalism.

It's been proven to be total wank - it was really an excuse to be a centrist Tory without the stigma of being an actual Tory, which was a real vote loser in middle England back in the late 90's and early 00's. It worked for ages, until the working class realised they'd been completely abandoned by 'their' party, and the lower middle class realised they'd been excluded from the property boom and that their kid's shiny new loan-paid degrees were becoming useless. It caused the rise of UKIP just as much as anything else did - the working class would (mostly) never vote Tory after Thatcher, but couldn't vote Labour anymore either, so ended up with the only party that spoke to them about something they could understand (lack of jobs and funding) by blaming it on immigration.

It's also why there's a massive disconnect between the Corbyn/Momentum Labour Party and the Parliamentary Labour Party - most of the PLP are Blairite, and literally wouldn't know what socialism was if it danced naked in front of them. The excuse is that 'real' socialism cannot win elections because Britain is an inherently conservative country, so you have to temper socialism with lies about not being socialist to trick people into voting for socialism.

What you always end up with is a committed capitalist who lies about having any interest in socialism to get votes, i.e. Tony Blair and Blairism.