Campaigns (or acts) are a series of playing sessions that follow the same party of player characters as they fulfill some grand story arc. Campaigns typically have a larger cast of characters, a map teeming with enticing locations and high personal or societal stakes for success… or failure!
Over the course of campaigns, the characters engage in quests to aid their civilization; build their status by developing ties with new allies; explore new territories; get stronger while gaining new skills and powers; obtain wealth and rare items, fight the bad guys; or simply goof off for fun.
Some campaigns only follow parties with lower-ranking players, while others play powerful superhuman characters. Still others start at white Rank 1 and climb the ranks all the way to red Rank 32 through overcoming obstacles and enjoyable roleplaying.
A one-shot story that can be completed in a single game session is typically known as a mission (or chapter).
A well-rounded campaign should have a few components. It may start a mystery or puzzle that forces the party to seek the truth. That may require a social arc, engaging in intrigue with unsavory characters — who may be friend or foe — to proselytize, recruit or network, or investigating (or bribing, or manipulating) informants or sources who may reveal secrets about an enemy stronghold.
It may also start by traveling to a new domain to explore, survey, adventure and survive in. It might involve engaging in trade, barter and cutthroat business practices to acquire wealth, a prized treasure or a MacGuffin.
And ideally, while anytime in a war-wracked world may be good for a fight, a good campaign should face a climax that involves infiltrating an enemy stronghold, where either stealth or combat plays a strong role, with possibly an escape from the stronghold being part of the denouement.