It's pretty simple actually. Imagine direct democracy, but with the option to delegate your vote to someone else, who can delegate their votes to another person, and so on. At the end of the day, the major powers aren't based on traditional parties but on layers of delegation.

The obvious danger here is its tension with the secret ballot. Currently, your boss can put all sorts of pressure on you to vote a particular way (even if it is illegal), but he ultimately can't step into the voting both with you. In contrast, with "liquid democracy", the chain of delegation may afford all sorts of ways to decide how someone "voted".