Synthesis, also known as 'orbs', is the primary method of increasing the power of a medal's Ability. By fusing identical medals or fusing with a Mickey and Brooms medal, the multiplier of that ability can be raised to increase the damage dealt. The synthesis level of a medal is depicted with yellow orbs beneath the Ability name. Each identical medal fused will increase the number of yellow synthesis orbs by 1, up to a maximum of 5 on a 6★ medal. A 3★ medal can have a maximum of 1 orb, a 4★ medal can have 2 orbs, a 5★ medal can have 3 orbs, and a 6★ medal can have 5 orbs.
For example, on the left is the base stats for Riku KH3D Version at 6★. Notice the attack multiplier is x3.10.
The Riku medal on the right is fully synthesized (notice the five yellow orbs), meaning that five total additional Riku KH3D Version medals had been fused onto it. The multiplier for this medal is x3.91, a significant increase in damage.
When synthesizing medals, you can preview the number of orbs which will appear on a medal after synthesis is completed. On the left, we can see that combining two 4★ Auron medals will result in one 4★ Auron medal with one synthesis orb.
On the right, we can see the effect of combining a 4★ Auron with a 6★ Auron. The 6★ medal will only increase in level, but no additional synthesis orbs will appear on the synthesized medal. This is because the two medals are not identical--if the medals have different catalog numbers (4★ Auron is #180, and 6★ Auron is #182), synthesis will not grant an orb. The only exception is the Mickey and Brooms medal.
When evolving a medal with synthesis orbs, the medal will retain its orbs. The Auron medal in the example on the left, when evolved from 4★ to 5★, will become a 5★ medal with 1 synthesis orb.
When a medal with synthesis orbs is synthesized to another identical medal, the existing orbs will transfer. If the Auron on the left is evolved to 6★ (becoming a 6★ medal with 1 orb) and then synthesized with the 6★ Auron medal with 3 orbs on the right, then 2 orbs will be transferred to the synthesized medal--one for the orb it already contained, and one for the medal itself.
Obtaining the full synthesis bonus on a 6★ medal require 6 total medals. The most economical way to obtain a fully synthesized 6★ medal is to combine the 6 required medals into 2 5★ medals (i.e. one 5★ medal with 3 orbs and one 5★ medal with 1 orb, or two 5★ medals with 2 orbs each), which will only require 6 Fantasia Mickey medals, 4 Good Fairies of the appropriate color, and 160,000 Munny, as opposed to evolving all 6 medals to 6★ and then combining them, which requires three times as many materials.
Upon clearing mission 350, fully synthesized 6★ medals can be further powered up through Guilt.