Quest givers are similar to vendors. Instead of goods, they trade missions and rewards. They can also offer some insights on the world lore, or give tips to the player. Characters that give side quests, ask for the player's help, or enable new narrative branches are a great addition to many games. They bring the world to life, giving the feeling that the protagonist is not alone in a static world full only of hostile creatures to defeat. They have needs, motivations, stories.
Obviously, there is extensive use of these characters in RPGs. Try to play a few RPGs or MMOs and focus on the characters that give you a quest. Note down what kind of quests they give and how they contribute to the development of the storytelling.
