Mounts can be used by players to increase their movement speed. They cannot be used in combat or inside dungeons. To ride the mount from your inventory, simply right-click it. Players seem to find it easier to attach it to their hotkey, so that traveling to and from places is quicker.
There are currently a lot of mounts and many different ways to get them. Some can be bought from other players (i.e. the auction house), some are offered on the Eden Crystal or Eden Gem altars, some are sold in the item mall or loyalty shop, and some are given as tiered spender rewards. There is a combat mount, the Silver Frost Tiger, the Golden Frost Tiger, and a dragon, for example.
The Grassland Alpaca is the first and free permanent mount available and can be obtained after completing the quest Alpaca's Friends. Players can accept that quest at level 13 and complete it and gain the mount at level 16.