I am trying to understand what is the deal with "full-frame" and what difference it makes...

Part of the confusion seems to be that you read the phrase 35mm equivalent and assumed it meant the focal length of the lens. In fact, that phrase simply refers to the 35mm camera format that started with the film cameras upon which DSLRs are based.

The photographic film used in most film SLR cameras is called "35mm film" because it's 35mm wide. The frames recorded on that film are typically 24mm high and 36mm wide, so a "full frame" DSLR has a digital sensor that has those dimensions. Because the 35mm format is ubiquitous, it's common to talk about lenses for other formats in terms of the lenses for 35mm cameras that would give a similar field of view.

So, when you read something like:

The iPhone 6 has a 29mm (35mm equivalent) lens...

just know that it doesn't mean that the lens is similar to a lens with a 35mm focal length, and it does mean that the lens is similar to a 29mm focal length lens on a 35mm format camera.

I am trying to understand what is the deal with "full-frame" and what difference it makes...

Part of the confusion seems to be that you read the phrase 35mm equivalent and assumed it meant the focal length of the lens. In fact, that phrase simply refers to the 35mm camera format that started with the film cameras upon which DSLRs are based.

The photographic film used in most film SLR cameras is called "35mm film" because it's 35mm wide. The frames recorded on that film are typically 24mm high and 36mm wide, so a "full frame" DSLR has a digital sensor that has those dimensions. Because the 35mm format is ubiquitous, it's common to talk about lenses for other formats in terms of the lenses for 35mm cameras that would give a similar field of view.

So, when you read something like:

The iPhone 6 has a 29mm (35mm equivalent) lens...

just know that it doesn't mean that the iPhone has a 29mm lens that's equivalent to a 35mm lens on your DSLR; instead it means that the iPhone has some lens that gives a field of view similar to a 29mm lens on a 35mm format camera (such as a full frame DSLR).