Job Level can be raised by spending materials: faint memories, statues, elemental crystals, weapon crystals, and job memories.
By leveling up, units' stats are enhanced and more panels on the ability bords get ready to be unlocked with spending Job Points.
Here is a list of required materials for each job level.
UR Units & Tier List
Starlight Elena
Sylvie
Reroll Guide: Tier List & Tips
Sephiroth
Astrius
Upcoming Unit/Vision Card Release Schedule