Ethereal items are only found in Diablo II: Lord of Destruction. Ethereal items are representative of weapons and armor (but never amulets, rings, arrows, bolts, bows, crossbows, Phase Blades or set items) crafted from other-worldly material. They are transparent, and can be magical, socketed, rare or unique.
Ethereal is an item flag, similar to socketed, and is not a prefix or suffix. When an item is ethereal, it gains a bonus to its damage/defense, has reduced durability, has reduced requirements, and is no longer repairable through conventional means.
The bonus to damage or defense is 50%. The new durability is half of the original +1. Strength and Dexterity requirements are reduced by 10 each. The sale value is reduced by 75% or more.
Ethereal items can be self repairing, but if the item breaks, the self repairing attribute will stop working and the item will stay broken with the durability remaining at 0. The same principle doesn't apply to ethereal Throwing Weapons with replenish quantity — even if you hit 0, the attribute will still work and the quantity will be eventually restored.
It is safe to give an ethereal item to hirelings, because equipment used by them will never lose durability.
Whether or not the ethereal condition of items transmuted with the Horadric Cube will be kept depends on the recipe used. As a general rule, recipes that keep the attributes of the original item, like socketing and upgrading recipes, will also carry the ethereal condition to the results, while recipes that generate a new item with new properties, like rerolling or crafting recipes won't carry the ethereal condition to the results. None of the Cube recipes that repair items work on ethereal items.
The socketing recipes for normal quality items present a bug if used with ethereal armors (body armor, helm or shield) that will apply an extra 50% bonus to defense. E.g. an ethereal armor with 100 defense will yield the same armor with a random number of sockets and 150 defense instead. These are often referred to as "bugged" or "eth bugged".