The origin of "Progressive Damage Methodology"

I guess what you are talking about here is the modeling of material behavior with the so-called damage. Damaging is usually considered an irrevisible process. The quantity of "damage" is just like the plastic strain, is an internal variable that depicts the extent to which the material is subject to re-arrangement, which is often detrimental. This process is of "progressive" nature, meaning, it is not occuring all of a sudden, which eventually leads to fracture. Decades ago, fracture is often regarded a sudden rupture, which becomes more accepted in now a days that damage accumulates over deformation - that is "progressive"

Your second question has something to do with length scale. Damage, as defects, are often considered at one length scale smaller, i.e. some heterogeneity. At structure length scale, damage may be small crack and notches etc.  At continuum scale, damages are usually voids, micro-crack and inclusions etc. And so on... At the continuum level, most commercial finite element codes have some "progressive damage model" at the continuum level that is convenient for you to adopt and play with.