It means social ownership (any form of ownership that allows distribution of the surplus to the employees or society at large) of the means of production.

There are both market and non-market socialists, who have differing opinions on whether the market should remain or be completely replaced by some sort of planned economy.

In basically all versions of socialism, the workplaces are democratic and managed by the workers themselves, but in terms of ownership this can vary between the workers owning their own enterprise, to the state (representing society at large) owning the MOP.

I'd Google Richard Wolff. He's a market socialist, but I've heard many on socialist threads say that he was a good intro to the basics of socialism. He's also been used as a launching point into non-market socialism, if that ends up being your preference.