In attempting to answer the question "What is Socialism?", I think it comes down to that what all socialist projects, whether Social Democratic, Anarchist, Communist, what have you, have in common is that they see Socialism as constituting freedom from economic determinism.
The Communist experience fits this less than others, since they had an articulated notion of Socialism which could be used to justify many things contrary to this notion, but the Third World Communisms were much better on this score. So, Socialism as freedom from economic determinism. The concept feeds from Marx's idea of history, i.e. history as being molded by the economic structure of society, with the assumption being that throughout history the economic substructure has been a subtle and sometimes hidden determining influence on the nature of the society. Through most of human history society's have been for the most part conservative in that they tend to conserve traditions rather than praise innovation; this conservative factor helps the economic structure to dominate over the society since the folkways and traditions which are being conserved serve the existing power and economic relationships of the civilization. The bourgeois society, according to Marx, was innovative in that it smashed the traditional conservatism of society and opened up the door for innovation and questioning; this opportunity for self determination free of conservative traditional influences could then be used to finally confront the underlying economic shaping of society, to take hold of it and to transform it so that it benefits everyone, rather than secretly benefiting a certain class of people, and that being done blindly and rather unconsciously.Socialism for Marx was, then, the freeing of humanity from dumb economic determinism which typifies all societies and the beginning of freedom for people to determine their own fates, to transcend the determination, to transcend economic materialism.
The main difference between Marx and liberal thinkers is that the liberal thinkers thought of freedom in a very general way, as freedom from unjust power in the abstract, without taking notice that simple power, as in State power, wasn't the only source of power around. Marx connected the liberal idea to an understanding of the structure and development of society, so that in order for the liberal idea to be fully realized there also has to be a fundamental change in the economic structure of society.
All socialisms believe in freedom for the individual, however they choose to manifest it, all socialisms believe in a fundamental change in the economic structure to facillitate that freedom, all socialisms which are worth something believe in socialism as an emancipation from blind determinism based on economic conditions and in socialism as the start of a commonwealth where all may develop freely, no matter where they stand in the structure of society.
One last thing, and that is that Marx seemed to believe in economic materialism himself, i.e. in the inevitable triumph of socialism as guaranteed by a crisis as predicted by historical materialism. Much ink has been spilled since Engel's death about the inevitability of this and that, as if history was a pinball game, but I think that this type of economic determinism is really a bourgeois concept. Before the socialists took it up the main proponents of this type of determinism were capitalist thinkers; you can find ideas of this sort in the works of Herbert Spencer, the founder of Social Darwinism, you can find them in the ideas of Malthus, in writers talking about the inevitable rise of capitalist progress in the early part of the 20th century and the later part of the 19th. I think that this whole thing is the last gasping breath of the old order, the conservative order which liberalism overthrew, trying to assert itself and that it should be laid to rest. Before socialism was inevitable the progress of liberty was inevitable. The problem isn't with either of them, the problem is with linking them to a particular fixed historical dialectic which automatically works out. Both are good, neither is inevitable. Socialism should be established because it's right, not because someone feels that it's inevitable. Liberalism and liberty, democracy, should be respected because it is right, not because it's inevitable either. As for the ethical systems which justify these two categories, work it out yourself; there are plenty of philosophers and thinkers who have written about social justice and ethical societies; it's about time that socialists got off the horse of not looking at moral and ethical issues because they believe it will inevitably be solved by the future society and instead look at the real world.
I don't want to end on a sour note so let me say that this framework, skeletal as it may be, can contribute to real proposals for change....
Hopefully socialists will be up for that, too.