Etherealness is a trait that indicates some incorporeality. They might have a Spiritform, like a Ghost, or they might only barely exist in this world (like, according to the lore, a Shadow Seer). The trait functions a bit like "Blink" from Dungeons & Dragons.
If a hit isn't magical, it has only a 25% chance (at most) to actually do damage; the Damage and Protection rolls are flat-out ignored, unless the 25% chance works. The hit still lands, though, so "on hit" effects (that are magical) still apply. Why isn't the chance zero? Because if it were zero, that would indicate that the fellow isn't able to interact with our world at all. Magical hits have that little white star next to their damage values, while non-magical hits from spells typically specify that they're nonmagical.
Aside from most weapons, what does Etherealness help you avoid?
Oh, and Ethereal fellows can also walk through walls. They're worse at Trampling, however, dealing halved damage.
All Spiritforms are Ethereal, but not all Ethereal fellows are Spiritforms. Spiritforms are especially incorporeal; not merely phasing out of reality in most instances, these fellows have to try rather hard to be coherent enough to land a hit. They cannot be made real, so:
Illusions are very similar to Spiritforms, being unreal constructions of light. They have an additional weakness, however, in that they can be disbelieved. These fellows are largely the same as the old Phantasms from Dominions 5, with 1 HP, Lifelessness, and vacancy; in Dominions 6, the old Phantasms are still Ethereal Magic Beings, but they're now Conjurations with souls and proper toughness.
On another note, Illusions will eventually dissolve, if a Glamour Mage isn't present to keep them around.