What's a Campaign?
A campaign is the entire story of a group of heroes told while playing the game. It starts with a campaign pitch from the Director to the other players. During the pitch, the Director tells the players about the setting where the game takes place and what kinds of stories the heroes will undertake.
If the players like the pitch, they create heroes and then the game begins! The Director prepares and runs adventures which are played out over a series of game sessions. During these sessions, the heroes play out scenes that include combat encounters, negotiations, montage tests, investigations, downtime projects, and more.
The best way to think of a campaign is to compare it to a film saga, a series of novels, or an epic television show. Each adventure that makes up a campaign is one film, book, or season of television in that series. Each game session is then an act of the adventure's film, a chapter of its book, or an episode in its TV season. Adventures might be tied together by an overarching villain who the heroes face in a thrilling final encounter. Or they might have connected goals, such as the heroes hunting and destroying evil artifacts, that tie them together in a campaign. These ties between adventures aren't necessary, but many players are drawn in by a cohesive campaign story.
Some campaigns are short, spanning only a single adventure or even just one session of play. Most last a good while longer than that, and contain multiple adventures. The longest campaigns feature many adventures and take the heroes from 1st to 10th level.
You're Not Being Tested
You don't need to memorize every single rule and exception before you start running Draw Steel. This is a big book, and you're allowed to use it while you play! Whenever a question comes up at the table, you can tell the other players, "Let me reference the old texts," and find the right answer.
You absolutely don't need to know every ability or feature that the heroes have access to. Let the players be the experts on their characters. And if a player is ever unsure of how an ability works, have them read it out loud so you can talk it through, or you can look up the answer together.