They flesh out the game's lore, if you actually take the time to read the text, that is. For example, the quest line in Drybone preceding the Ifrit battle relates to your character's progress in the investigation of suspicious Amal'jaa activity and abductions, and your pursuit of a traitor. Sometimes this involves doing small chores for villagers to gain their trust or cooperation. For new players, this is a valuable source of experience points and gear, which is needed in order to actually get a chance at the next major battle or dungeon.

Now, if you're a v1 player with a level 50 character, and you just speed-close the quest dialogue or skip cutscenes to move ahead as quickly as possible, I can imagine these quests would seem pointless. But I could also argue you're playing the game all wrong.