You may be confusing the name of the modifiers, there is no "UV Unwrap" Modifier, there's only a UV Warp and a UV Project modifier.
Unwrapping, as you already know, is used to provide texture coordinates to an object so Blender knows how to apply a certain texture to the mesh geometry.
It is sort of a "destructive" process in the sense that if you change the object's geometry after unwrapping you may need to adjust it afterwards or totally unwrap any newly created geometry.
It is however the only way to obtain correct texture coordinates for complex shapes.
For certain corner cases or specific applications you can use the modifiers for certain tasks in parallel with unwrapping or in its place, but they are not true replacements for unwrapping.
UV Warp Modifier
The UV Warp Modifier, added to an already unwrapped object, uses two other objects to modify or manipulate an already existing set of UV coordinates. It may be used when you want an animated texture, want the UVs to somehow react to other objects, or edit UV Maps directly from the 3D view with interactive visual feedback.
UV Project Modifier
The UV Project Modifier is used as a replacement for UV unwrapping to generate a UV map as if a certain image was being projected over the mesh from a certain point in 3D space, like a true slide projector. It is often used for video mapping and inserting 3D objects into a real filmed scene.