Socialism is a badly misunderstood word. Does it refer to a concept, a philosophy, a political system, an insult? Here’s an excellent explanation of the basic premise of socialism, such that I could use with undergrads (and other people who need it).
In my view, the most fundamental characteristic of socialism is its commitment to the creation of an egalitarian society. Socialists may not have agreed about the extent to which inequality can be eradicated or the means by which change can be effected, but no socialist would defend the current inequalities of wealth and power.