Hobbies And Interests
Efficiency
Consider a typical quest chain. The first quest asks you to complete a specific task, such as killing a certain amount of enemies, then return to the quest giver. Once you complete this first quest, the quest giver offers you another. If you complete the first quest then accept the second one and immediately start working on the second quest's objectives, any group members who haven't yet accepted the second quest will be left behind. This can result in the group having to repeat certain tasks or kill additional enemies. For example, if the second quest asks you to kill 15 of a specific enemy and you start killing them by yourself before any other group member has accepted the quest, the enemies you kill won't count for the other group members. The group will therefore need to kill additional enemies so that everybody can complete the second quest.
Escort Quests
Escort quests are a special type of quest that requires you to escort a nonplayer character (NPC), usually the quest giver, to a specific destination, defeating any enemies along the way. Often, players must have completed the quest that led to the quest giver before they can accept the escort. If you complete that quest then accept the escort immediately without waiting for all group members to also complete the quest, the NPC will start moving and the other group members will be unable to accept the escort quest.
Arena Quests
Arena quest chains, such as the "Ring of Blood" in Nagrand or the "Amphitheater of Anguish" in Zuldrak, work in a similar way to escort quests. The objective of these quests is to defeat a series of strong enemy as a group in order to obtain powerful rewards. Each enemy is the target of a separate quest. If you complete one of the quests and accept the next one without waiting for the rest of the group to do so as well, the next battle will start and the other group members will be unable to complete the quest and accept the next one, forcing the group to defeat each enemy twice in order to complete the quest chain for every member.
Considerations
Even if you feel that other players in your group are too slow in completing and accepting quests, you should still wait for them rather than carry on by yourself as if the other players in the group didn't matter. There are several reasons why they may be slow in completing quests; they may be lagging, or they simply may be interested in reading the entire quest text rather than just checking the quest objectives and moving on. Being in a group makes questing more efficient, and some quests would be almost impossible for you to complete by yourself. If the group you are in is too slow for your tastes, find a different group or quest alone rather than sabotaging the group's efforts.