Wizard's magic orb becomes more powerful, pop [sic] up to seven Bloons at once.
~ BTD4 Description
Shoots larger and more powerful magical bolts.
~ BTD5 Description
More powerful magic shots move faster and can pop more Bloons.
~ BTD6 description
Intense Magic is the first upgrade on the first path for the Monkey Apprentice in BTD5. As it says in the description, this upgrade will let the Monkey Apprentice pop 7 bloons and be able to pop frozen bloons (in BTD4, as all other versions allow popping of Frozen Bloons by default). In BTD5, the orbs flash in purple, blue and yellow.
In BTD6, this upgrade is the first upgrade on the third path for the Wizard Monkey. It gives the Wizard with +5 pierce to each bolt, giving a total of 8 pierce for each normal bolt attack (7 to 12 for Arcane Mastery, and 11 to 16 for Archmage). In addition, projectile speed for all bolt attacks are increased. Currently, Intense Magic does not affect any fire-based attack except Wall of Fire and Dragon's Breath (Fireballs and Summon Phoenix are both excluded). For Wall of Fire, it grants +5 pierce, while Dragon's Breath flames are granted +2 pierce.