An item can be upgraded to increase stats or apply effects such as HP Drains, Paralyze, Sleep, Poison, Seal, Knockbacks, and various resists. Keep in mind that for HP drain and inflicting effects, only items applied to weapons will work. Stats and resistances will be applied regardless of weapons or armor.
In addition, keep in mind that the more you add on to the weapon, the lower the success rate. This applies even more with really rare items. Therefore, it's recommended to upgrade an item with high difficulty upgrades first.
You can upgrade the item up to 9 times, and each time the level will increase by one for the weapon, increasing stats and value. At Lvl 10 the weapon/item cannot be upgraded further.
Via upgrades you can also modify the item's affinity/element. For example, Saint Axe is a Light element weapon, but when upgraded with a Love item such as Love Crystal, it will become a standard, non-element weapon.
Additionally, if a staff is upgraded with an item of a monster, the weapon's charge will use the monster's abilities. This works for bosses' abilities as well.