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
Upcoming Unit/Vision Card Release Schedule
EX Job Guide
UR Vision Cards
Helena (Black Witch)