Home Campaign: A series of RPG sessions that share a common theme, setting, and background played by the same players (with the same respective characters) and traditionally a single Game Master (DM/GM/Storyteller/etc.). While the rules as written may apply, house rules (rules specific to a specific group of players) often develop. Home campaigns are often very focused around the personal goals of the players' characters.
Organized Play (OP): A campaign, often sponsored by a company to promote their products, that relies upon standardized mods, character creation rules, and ultimate authority resting not in the Game Master but the head of the campaign. In OP, people often function both as player and GM at different times (often playing and/or GMing the same mod for XP credit). OP campaigns may have an ultimate focus, but it is determined by the campaign staff and writers and not tied to what the players (or their characters) want.
When it comes to RPGs, nothing competes with a solid, reliable, and enjoyable home campaign played with friends. That, however, seems to be a luxury that few can afford. It takes a lot of time and effort to craft stories from scratch – or, if you're Dave Jendrusiak, you borrow liberally from movies such as Willow (1988) and a variety of mid-grade fantasy novels to cobble a story together – and I'm betting that most adults just don't want to make that kind of commitment. It isn't just the DM/GM/Storyteller/whatever-other-title-is-used-for-the-person-running-the-game who has to put in the time to make that work. There is a very personal investment, and that requires a serious time commitment. OP play is much more willing to let the player decide how much of a commitment he or she wants to make. It may be a little harder to play as much as one wants when opportunities are limited to game days or conventions, but those allow for the player to step right in and participate as he or she sees fit. The person who only wants to be a player (and never GM) doesn't have to learn more than the rules for his or her character and enough about the setting to understand the basics of the game world.