They know precisely what it means. It's we who struggle to figure it out. Democracy is a form of government in which the majority vote makes the choices about policy. This is the form of government Plato explicitly advised against because it enables the 51% to tyrannize the 49% minority. It's two wolves and a pig deciding what's for breakfast.

The Democrat party loves this idea, but they need to project the illusion that they represent the majority. They've been doing this for decades with their "we represent the working man" rhetoric and their racial "big tent" rhetoric. They position themselves as speaking for the masses.

Where have we heard that before? In Russia, in 1917. As the Romanov dynasty was collapsing under pressure from fighting the Germans in WWI, the Russian empire was failing economically, couldn't feed its soldiers, and autocratic authority was no longer enough to keep people in line. Marxism took deep root and soviets (local communal governments) were set up. Two groups emerged with different visions for how to change things the Bolsheviks (tr: "the majority") and the Mensheviks (tr: "the minority"). Turns out the Bolsheviks had better branding because although they had less support in terms of votes, they had rhetoric on their side and projected power. Ultimately, the revolutionaries rallied to them. That's right, the minority asserted that they represented the majority democratically, and used that to set up the USSR.

"Our democracy" means precisely that, the government they want and they don't share power.