Chris Matthews asks Hillary Clinton, who can't answer. Apparently Matthews had already asked her puppet, Debbie Wasserman Schultz, and received the same non-answer.
The question isn't hard to answer, so it's interesting that these figures are dancing around the answer.
A Socialist believes that, to the greatest possible degree, the means of economic production should be owned by the Public and not by individuals or corporations. Practically this means that the government should own the means of production as much as is practicable.
A Democrat believes that, to the greatest possible degree, power should be invested in the citizenry broadly considered, rather than in some elite. It is opposed to monarchy, aristocracy, but also technocratic systems in which judicial or lawyerly or scientific elites rule over us as our betters.
There is thus no necessary connection between the ideologies. One can be a non-democratic Socialist, as the Communists often were. One can be a Democratic Socialist, as European parties sometimes claim to be. And one can be a non-socialist Democrat, as in fact most American Democrats have historically been.
The connection between the two is nevertheless not accidental, even if it is not necessary. Aristotle explains in the Politics that democracy is government by the many (rather than the few or the one), and that the poor are always more numerous than the rich. One of the thing the poor tend to want from government, even in ancient Greece, is for it to redistribute wealth to them from those who have it currently.
Aristotle warns against this tendency strongly. It will destabilize the state, he says, for the rich to be deprived of both power and their property. They will respond by hiring mercenaries to overthrow the democracy, which will lead to the harms of political instability or war. On the other hand, in a system that is governed by an elite (an aristocracy, for example), redistribution of wealth is an important point of public policy. The poor must be made physically secure from starvation and the harms of poverty in order to support a state that denies them political power. They can cause an insurrection too if their interests are completely ignored by the powerful.
Thus, Socialism should be regarded as the sickness of Democrats. It is an illness to which they are particularly prone. That does not mean that Democrats are wrong to favor government by the many. It just means that the position entails certain risks which have to be guarded against faithfully. Other positions entail other risks, so it is not a unique failing of Democrats that such a risk exists. This one just happens to be the one to which they are especially likely to fall prey.
As, apparently, they are currently doing.