The type/color determines how much damage you deal or defend against. Each type has its own rock-paper-scissor diagram. For examine, STR (red) is strong again PHY (orange) but weak against AGL (blue). If you're using a red character, you'll deal extra damage against a PHY character. However, if your opponent is a AGL character, your attack will be guarded and you'll deal lesser damage. Attacks to other types will just deal normal damage. Characters evolved via Z-Awakening will have a “Super” or “Extreme” sign to their type. This allows them to deal even more damage against the weak to their type and even more endurance against the type they're strong against.
Take note that the Ki Spheres doesn't affect the damage output of a character towards the target. For example, if your purple character collects red spheres to attack an orange character, your attack will still be blocked because in the end, your character's type is weak against your target.