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Hierarchical assembly of galaxies (or hierarchical merging) is a general model of the development of large galaxies, that after some galaxies formed, they often combined and the largest observed galaxies are result of such galaxy mergers. For example, the Milky Way has satellite dwarf galaxies that can collide and merge with the Milky Way, and Andromeda is on course to collide with the Milky Way in the future, perhaps to form a larger galaxy. Such merging is pretty much accepted but specific models differ on how much such assembly contributed to the current state of galaxies.
The term hierarchical clustering is also used, probably typically referring to the analogous notion that galaxy clusters form from smaller groups.