Fusion is a special process of combining monsters to increase their strength. There are currently two types of fusion, standard Fusion (usually called Fusion) and Fusion+.
Fusion allows you to combine one or more monsters into a single monster in order to increases the experience of the base monster which in turn can raise the monster's level. As a general rule, the higher level of the monster, the more experience needed to gain the next level. Also, catalyst monsters of the same type as the base will provide a higher amount of experience when fused.
Fusion+ is a special type of fusion that requires two of the exact same monster. Fusion+ can create a stronger version of the base monster. Rumors exist that Fusion+ could also create a new monster altogether. Fusion+ is expensive, however the cost can be lowered by first leveling up the base and catalyst monsters. The resulting fused monster will always be level one.