Socialism is a political and economic theory that advocates for the means of production should be owned by the community as a whole.
Socialism seeks to elimanate a market based economy and thus eliminates private property rights. It is in many ways the opposite of capitalism.
Because the system advocates for community to be held in higher regard than the individual, it is sometimes best understood as 'collectivism'.
Democratic Socialism is a marketing phrase to hide the intention, and make socialism seem more palitable to the general public. Though, it's important to point out that former leaders of Socialist countries also called themselves 'Democratic Socialists', Pol Pot, Stalin, Mao - three of the most represensible leaders of the 20th Century.