Probably the best answer is whatever Bernie Sanders says it is as he is by far the most famous person ever to adopt this term as a label for his beliefs. There is a group in the US baring that name, the Democratic Socialists of America (DSA), which has been in existence since 1983. But while its membership ha since then generally fluctuated between 4,000 and a bit over 6,000 through 2016, its membership had surged to over 45,000 by 2019, clearly responding to Bernie's identification with the term, even though as near as I can tell, he has not been a member of the DSA.
If one goes to the Wikipedia entry on "democratic socialism," one finds claims that it originated with the utopian socialists and chartists in the early and mid-1800s. Certainly many of these groups supported democracy and also some sort of socialism. For that matter, Karl Marx also in many writings supported democracy and socialism, although in other places Marx sneered at what he called "bourgeois democracy," and we know many regimes claiming to be inspired by Marx have not been democratic, unless one wants to call Leninist "democratic centralism" to be democratic, something most of us would not go along with, and current DSA types would not go along with.
The Wikipedia entry also includes the British Labour Party from its origins and also various social democratic parties, although many "democratic socialists" like to argue that "democratic socialism" is not the same thing as "social democracy," even though many self-identified democratic socialists, including Bernie, point to social democratic nations like Denmark as role models when asked what they are talking about. Of course self-identified "social democracy" has been around since the late 1800s in Germany with the still-existing German Social Democratic Party, although its ideology has changed over time. It officially linked itself to Marx as recently 1959, even though the Wikipedia entry on democratic socialism includes the "revisionism" of Eduard Bernstein around 1900 in the German Social Democratic Party as another example of democratic socialism.
A more recent example according to Wikipedia is the UK Labour government under Clement Atlee in the late 1940s when nationalized several major corporations and established still-existing socialized medicine, even as Margaret Thatcher re-privatized most of those companies Atlee nationalized. However, the Atlee Labour Party never used this term to describe itself, and neither did any of these other earlier groups or individuals mentioned in the Wikipedia entry, although it looks that Jeremy Corbyn has adopted the term and connected his views with those of Atlee.
So when did the term actually first appear? As near as I can tell it would seem to be shortly after 1970, and it would seem that is when Bernie Sanders took it on as his view. Wikipedia identifies Michael Harrington as its main developer, especially in 1973 when he was the main organizer of the Democratic Socialist Organizing Committee (DSOC) as a section of the Socialist Party of America (its earlier leaders such as Eugene V. Debs and Norman Thomas also show up in Wikipedia entry, although they never used the term, as near as I can tell). When the modern DSA formed 10 years later, it came out of a union between Harrington's DSOC with about 1000 people out of the New American Movement, with Harrington being the most prominent person involved with this.
However it looks like the term appeared slightly earlier, in 1971. This was with the formation of the Liberty Union Party of Vermont, which also still exists. It has described itself as being "democratic socialist" from the beginning, and Bernie joined it back then and ran as its candidate for several office, including governor in Vermont in the 1970s, even though he left the party in 1977. But it would seem that he has identified himself with this term since then, which may make him even more of a founder of it than the late Michael Harrington, who died in 1989.
So, with all this history this still brings us back to "what is it" besides whatever Bernie Sanders says it is? The DSA website offers a variety of possible meanings, although all of them involve political democracy, although some also call for "workplace democracy."
Clearly the murky part is the "socialist" part. Again, some are fine identifying it with social democracy, which does not call for nationalizing means of production, the classic definition of "socialism" from Marx and Engels, nor any imposition of planning or commands, but rather a large welfare state, along with liberal views on social issues. But the core part of the DSA website calls for "social ownership" of the means of production. But this apparently can mean either public ownership as in classical socialism or workers ownership and management as with cooperatives, or even possibly ownership by consumers. There is also a call for "decentralized planning" with this to be done democratically, but ultimately probably operating within a largely market economy.
If the Green New Deal is an example, there is less emphasis on nationalizing means of production, but more use of command elements in the economy, along with a large expansion of the social safety net. The use of command elements are linked to the environment and climate change, with invocations of how the US economy was run during WW II, which was indeed a temporary command capitalist economy. Ironically, although it is not widely recognized, large parts of current US environmental policy actually do follow command policies, especially in the form of strict quantity controls on pollution emissions rather than taxes or cap and trade.
Anyway, while the term is now very popular, it is really quite recent in usage and also pretty broad in what it actually means, a concept still in development.