Junctioning a number of Blizzard spells to Strength will raise its value. Also, junctioning a more powerful ice spell like Blizzaga will boost the attribute more than a lesser spell. In addition to boosting attributes, elemental magic can junction to a character's attack and defence. A character can be thus do fire damage with his weapon by joining Fire magic to that character's Elemental Attack ability. Similarly joining Fire magic to the Elemental Defence ability can augment a character's defence against fire-based attacks.
Some foes are more susceptible to specific magics.
The Status Attack and Status Defence abilities work the same way, except that the junctioned magic relates to changing a character's condition. For example, a character with Sleep spells junctioned to Status Attack has a chance of putting an opponent to sleep. Similarly, junctioning a spell like Death to Status Defence would help protect the character from the effects of death magic. GFs have their own levels, and they earn experience in battles along with the soldiers. This allows you to build up a GF with one character and later junction it to a different character while keeping the its accumulated levels and abilities.