There may be many purposes for democracy, but there is only one that really means something, and which is the sine qua non of democracy: Consensus creation.
Without consensus, we have nothing. All the adversity unleashed by campaigning, all the (sometimes mock-)animosity between members of different political factions or parties needs to eventually come down to one thing: consensus.
We need to work together, and democracy, ideally, can make this happen if it is structured in such a way that consensus is inevitable. It will be annoying, but productive, and the only real way to make decisions stick. Compromise for consensus’ sake is a real sign of strength, because, to quote former Chancellor Kohl, “what’s important is that which emerges in the end.” Results matter, and you get lasting results only with a compromise.
You get to compromise through humility, which is nothing else than the realization that you yourself could be wrong. Democracy means that you need to realize that the people may be smarter than you are. Once you get over your own ego, you’re ready to truly accept democracy as the only system creating lasting, sustainable change through consensus.