Mounts in Forsaken World allow you to travel around much quicker than you would on foot.
At level 20, you will get a quest to receive a free timed mount that will last you 1 week. This will help you travel around as you continue leveling up, and give you a taste of the benefits that owning a mount includes. You can also get a free mount by gaining enough faction reputation for your racially specific mount. You gain reputation by completing various daily quests, and progressing through the storyline.
You can also simply purchase a mount out of Eyrda Boutique with real world money. There is a wide variety of mounts available in this boutique, so check them out by hitting the (default) "J" key and navigating to the mounts tab..
Using a mount is very simple. Right-click the mount icon in your inventory and you will begin to summon your mount. Right click it again to dismount when you want to get back on your feet.