There are two basic types of equipment, normal and rental. Rental equipment, rented from Mist Merchants, cannot be strengthened with enchantment stones, manastones, or godstones, whereas normal equipment can.
Equipment items are ranked by their quality, or rarity, in Aion, identifiable by the color of the item's name. For non-equippable items, the colors are the same. Gray named items that you can't equip generally have no use in the game, and should just be sold to vendors for kinah.
For more detailed information about quality/rarity, see the Rarity page.