NPCs have a lot more to say than you might think.
Greeting text is often skipped in favor of getting immediately to a quest, the vendor interface, the flight map, etc. And getting to those things quickly is great! But this means you sometimes miss out on some interesting dialog. So why not have the best of both worlds?
Gossipmonger grabs the text you would have seen and puts it alongside whatever it is WoW thinks you're in such a rush to get to. If you really are in a rush, then you've lost no time as what you want is there, as normal — but if you're interested in reading some flavorful, often humorous dialog, now that is there for you, too.
The screenshots show just a small sampling of what you're missing out on by skipping NPCs' greetings. (Besides, those NPCs have feelings, too! Maybe. Okay, not really.)
Another feature is more focused on convenience: "Quest Jumping" lets you click the dialog options shown in the "gossip bubble" frame we add to navigate directly between different quests (and other dialog options to a degree) without having to close the frame, talk to the NPC again, and find that option.
Finally, Gossipmonger includes a filter system for advanced users who know a bit of Lua, letting them create custom filters to use instead of or in addition to the standard behavior. Custom filters can do many things. For example: automatically selecting a specific dialog option when talking to a certain NPC; automatically selecting quests that you are ready to hand in; checking if you're holding a key down (e.g. Shift) while talking to a guard who gives directions and, if so, asking the guard where the inn is; or even preventing the gossip bubble from showing in certain circumstances (so dialog that you find only clutters things doesn't get in the way).