I mean, do you want the real answer or the answer the meaning that the dems are saying?
When a dem says they’re a “democratic socialist”, they mean almost exclusively that they’re a social democrat. This also ties in with what most americans (people?) mean when they say ‘socialist’, that is, they believe in regulations, a strong welfare state, and (non-state) capitalism (that is, the means of production such as factories and farms should mostly be in the hands of an elite class of ‘capitalists’ who operate these in order to make a profit,) as the primary economic driver. So the end goal is, as you often hear, Sweden. Relatively high taxes, very strong social safety net, but still capitalist in character.
Properly, however, democratic socialists are socialists (that is, they believe that the workers themselves should own the means of production.) The reason you tack on ‘democratic’ is in order to distinguish from what I’ll call the Leninist school of thought (as opposed to specific ideologies such as Marxism-Leninism, Stalin’s school, Trotskyism which had its own flavor, Juche, etc.)
The primary factor of Leninist schools is the presence of a ‘vanguard party’, a group of people heavily invested in moving towards a communist society whose job is to guide all the proles on this journey. This pretty much always entails some form of state capitalism as the primary economic engine. That is, a lot like the capitalist mode of production, but things are run by the state nominally to build the economy enough to get to the point where we can turn this whole thing over to the people, referred to as the “withering away of the state.” This isn’t universal, however, and there were states such as Yugoslavia which took a much more positive view of the workers and allowed them to manage the state-owned companies (read more here.) My understanding is that Cuba also has some more democratic and less party-centric leanings, but don’t quote me on that.
As far as democratic socialism proper, it’s hard to give you a proper, specific definition. It’s essentially a catch-all term which means “not leninist/authoritarian” that ranges from Rosa Luxemburg to the original UK Labor Party to Proudhonian mutualists to syndicalists to anarcho-communists to, interestingly enough, Helen Keller and Albert Einstein.