the issue is that (due to politicians being politicians) the word has been diluted to the point where "socialism" is both red and blue at the same time. (and no, I don't mean novel mechanical refractive properties.)
Salmon is correct as to the original definition. These days, that flavor of socialism is more properly known as "Marxist Socialism".
We also have "European Socialism", and a few others.
What exactly IS socialism? In the modern climate, it essentially is an umbrella term for the desire for government to be supportive and actively engaged in the maximization of assuring that basic civilians are empowered to interact meaningfully with the rest of the societal framework. In this way the government creates institutions and policies that are "Pro society", and thus "socially oriented"; ergo "Socialist".
Take for instance:
a properly functioning FCC, rather than one that panders to big media companies and ISPs.
Copyright rules that serve their purpose without becoming corporate welfare at the expense of culture
Healthcare systems and treatments that actually serve the public instead of a wealthy class's bottom line
Public education that actually works at educating young people, rather than being a tool of the state for indoctrination, or of the wealthy class to generate mindless workers
Employment rules that actually protect workers from financial and material abuses by their employers
Reforms of antitrust policy to go after abusive market players and foster competition
and of course, the oft-cited-- Reforms to public welfare that assure that people actually receive the help they need, when they need it.
At face value, these all seem like no-brainers that anyone would want. All of them are "Pro-social" in context-- The government and big finance get very little out of any of them except lots of work, and or less profits and more oversight.
Since they ultimately revolve around "taking something away" from the empowered wealthy classes, to promote a more healthy society overall, they get smeared with the "marxist socialism" brush, which has a guilt by association PR problem, due to the running track record extreme failure that extreme implementations have had in the past (USSR, Cuba, Venezuela, China, etc..) no matter how wildly divergent from the core principles of marxist socialism those governments have ended up. The desire to not lose the power and ability to institute quid pro quo via the lobby system, the ability to directly coopt a regulatory body (in the case of BOTH the FDA *AND* the FCC), and to control the narrative (via the for-profit press) which this demographic currently enjoys, this mis-appellation has become pathological, concerted, and even fervent.
At some point, when your current system is so ragingly antisocial, ANY policy that seeks to restore previously lost social freedoms or powers to the masses of society becomes "Radical socialism!(tm)".
For me personally, I draw a very important distinction between "No, you do not get to engage in shameless anti-societal behaviors for personal enrichment; that is sociopathy" and "I'm gonna help myself to all your bank accounts." Modern socialism has much more in common with that first one than the letter one. However, to those individuals and demographics that pad their bank accounts using the practices being taken away, they appear very much the same thing; It is this that must be exposed and held to account. I do not propose raiding private accounts. Quite the opposite in fact, I propose preventing the powerful from exploiting the weak for profit. The powerful just feel that this is functionally the same thing (because they are sociopaths.)
Ultimately, this "Pro society" angle is why the term originally began to become diluted in the first place, however. Most everyone agrees that shameless exploitation (such as occurs via naked capitalism without meaningful oversight) is a pathology. What most everyone cannot agree to, are a workable set of norms and rules on how to prevent this in the face of a continuously changing technological frontier, that enables both the society AND the powerful, in unpredictable and profound ways. (Such as social media, regenerative medical technologies, alternative energy technologies, etc.)
Since government does not have a crystal ball to look into, it has difficulty predicting when it needs to say no to "Just a little more welfare spending-- Some people are still disadvantaged". Because of this, well meaning governments can completely destabilize their internals and become insolvent. There is a disconnect between the plutocrats and the rest of society about where that line is.
This is why there are so many flavors of modern socialism. (Eurosocialism, anarchosocialism, et al.)
It sounds to me like what you are REALLY asking, is what is the US Left's (Eg, Sanders, Warren, and Co.) flavor of socialsm.
Basically, it boils down to that short list of "everybody sane, who isn't well entrenched as a power abuser would want these" features cited way up top in this post, and the necessary legal and government policy changes required to satisfy them.