Level 60 (previously 50 before the expansion!) is only really the start of the game! After that you can do the 24 people raid dungeons (for item drops mainly, but also weekly grade V materia to keep/sell), new extreme primals to unlock weapons and bird mounts, new dungeons to unlock weekly currency to buy better gear, as well as new gathering nodes and new crafting items.

I'm not explaining very well I'm sure, but basically getting to the highest level is just warmup!