It began as basically an Edwardian 'socialist but anti-revolutionary' group of bourgeois and petit-bourgeois thinkers. They were overwhelmingly middle class or above.

The key difference (and sticking point with other socialists) was that they believed in 'gradualism', not revolution. They believed that socialism would only be achieved by participation in the current political and electoral system, in order to spread socialist ideas through government, education, media etc. Their first issue and aim was arguably a reasonable one - there was no left wing never mind socialist party in British politics, just the Tories and Liberals.

Even some high profile members who were original believers left the Fabian society and grew skeptical of it pretty quickly though. H.G. Wells left after disillusionment with what he saw as a middle-class party not sufficiently different from other bourgeois parties.

And things got worse from there.

They supported the Boer war, and not just out of some fear of being branded traitors. They made their position clear by arguing that empowerment of the working classes in Britain would create a 'new imperial race' that would fight Britain's imperial wars and expand its empire around the globe. It was at that point that Bertrand Russell left in disgust, citing it becoming an imperial project as the reason.

They were admittedly a major part of the creation of the Labour Party at the turn of the century, but they were just one third of it, and plenty of people have argued the most problematic third for the advancement of socialism over the other two founders - the Independent Labour Party and the Trade Union Congress (not that they're without criticism either). And their reformism did gain some degree of popularity and results, especially around the building of social welfare and introducing ideas of social justice into the political mainstream and national identity.

It always lacked real solidarity though, fracturing over it being a nationalist, imperialist project. Fracturing further over the need the be anti-Stalinist. Then over more militant trade unions and wildcat strikes. And so on. Lots of people would point to the Fabian element in the Labour party as the wedge in the door that kept it open for the wholesale neoliberal takeover in the 1990s onwards.