They're summoned from oblivion, I know that much. Hence the daedric appearance. But what are they exactly? They look like spectral forms of weapons. Like they exist in your hand but are technically just apparitions. But somehow they still hurt people?...

Also, they glow purple. I've seen people have assassins that use bound bow/sword and they stick out like a sore thumb. This is what really made me question the nature of this magic. Are they invisible to others or something?

They can see the weapons, it is just a conjugation spell, try it and find out. Sometimes you find enemies that use bound weapons, such as the Falmer, but they are in plain sight, no hiding.

I think they sort of ~lend themselves~ from Oblivion, sort of like Summon Spectral Assasin.
I think they are visible to others, but you'd be dead by the time you can even question them

A bound weapon is summoned from another plane of existence. In order for objects that are summoned from plane A to exist in plane B, they need to be bound to something that exists in Plane A. This is why when you unequip a bound object, or dismiss a bound creature, or the creatures caster dies, it vanishes. The pathway between planes of existence is extremely volatile, which is why any summoned object or creature can only exist in another plane for a certain amount of time. Objects or creatures summoned to another plane still physically exist on their primary plane, hence why after their death, dismissal, or being unequipped, you can re-summon them. Even though a summoned object appears ethereal, because it was summoned, it has physical presence and occupies physical space. Which is how bound weapons are able to harm opponents despite their ethereal appearance.

Portals are the exception to this rule, as a portal is a doorway that allows physical objects to pass between planes of existence. Anything that passes through a portal now exists in the plane they arrive in.

" I've seen people have assassins that use bound bow/sword and they stick out like a sore thumb. This is what really made me question the nature of this magic. Are they invisible to others or something? "

You answered your own question there as well

I thought I read a book that said that bound weapons were actually lesser Daedra.