Public events are random instances that player guardians will encounter as they explore Destiny. Their objectives include defending zones against enemy waves, culminating in a final boss. Multiple fireteams will be involved, making a public event a very large scale occurence. Public events can be a good source for upgrade items, engrams and rewards. It appears now that they are timed and if X amount of people are in the same area at a proposed time an event occurs. Here's a handy tracker, so get your fireteams together and reap the rewards. Big thumbs up to lax20attack on reddit.