In World of Warcraft each race has his/her own mount which is a pet found in the Azeroth landscape which they have the ability to tame and ride around with. For instance, on the Alliance faction, the humans have access to horses, while on the Horde side Trolls have raptors. Each of the other races also have their own particular pet to ride. To able to ride you need the skill of riding which can only obtained once a WoW character has reached level 40.
In part mounts are acknowledge as status symbols for players who have reached the half way point of the game at level 40 among WoW players. As a matter of fact, it is always the goal of attaining my mount (especially my very first one) that gives me the motivation to grind away at the games quests and slaying of monsters while half way through the game.
But to the point, the best advantage of the mounts give you is to enable you to travel over land so much faster than by merely walking or running around. On top of that evading monsters is that much easier making game play less stressful when you are trying to get to a far flung destination. From time to time it is still possible for some monsters to knock you off your "steed" and force you to fight, but 90% of the time you will out run them. Also in certain enclosed places like inns, instance runs, quest buildings, neutral towns etc, it is not possible for you to get about on your mount.
Another advantage is that if attacked it will be your character taking the damage and not the mount, so if you die there is no need to re-summon it, as a Hunter or Warlock would with their pet or minion, or even having to buy another. The other great thing about owning a mount is that each different race can pick from a variety of mounts. At levels 60 and 70 there are even more better faster ones you can pick provided you have learned the necessary skill to ride which is easy enough if you have the gold to pay the riding trainer. Also depending on how exalted your reputation is with another race in your faction you might be eligible to ride their steed, ram, raptor, horse etc. Not to mention, both Alliance and Horde races can't their rival faction mounts.
There are some quests where you are able to obtain rare mounts like the "Black Qiraji Battle Tank" in the "Silithus quest" (obtained at around level 60) that will further enhance your character reputation in the game and in the eyes of other players as well as netting you an unusual looking mode of transport. Instances also provide rare pets you can ride like the "Fiery Warhorse" in Kharazan which alas only drops at the rate of 1 in a 1000 kills.
It is undeniable that there are many other examples of world of warcraft mounts, from turtle to fun ones introduced at special times of year like the rein deer is at Christmas or the flying broomstick at Halloween. This is what makes world of warcraft the great and unusual game that it is. The depth even when it comes to characters transport is varied and detailed and very entertaining.
As above, we best hope that you can gain benefit from our discussion.