As I understand it, in Aristotle's context:
- "generation" means "creation" (also in the sense of "composition"/"association")
- "corruption" means "destruction" (also "decomposition"/"dissociation")
The overall issue where these terms play a central role is that of the nature of the observable world -- what are things made of and how do they come into being.
One of the principal questions that Aristotle addressed was whether the process of "generation" of new objects (accompanied by destruction/"corruption" of old objects) is something different from the process of "alteration", in which old objects undergo change to become new objects.
Aristotle identified one group of Greek philosophers (those who thought that there was a single fundamental material "principle" of all things, e.g. Thales::water or Anaximenes::air) as compatible with the belief that "alteration" is the only possible way for entities to come into being, since (following the single-principle logic) all objects must be the different "alterations" of the same primary substance.
He identified another group (those who thought that there were multiple fundamental material "principles/elements", e.g. Empedocles::4 elements or Democritus::atoms) as compatible with the belief that "generation" is the primary mechanism of coming into being (and is different from "alteration"), since (following the multiple-principle logic) objects must be compositions of the multiple material principles/elements (that do not themselves change).
Aristotle based his own account of how objects ("substances") come-to-be on his conception of substances as "having" matter and form (which are two of his Four Causes).
- A substance can come into being as the result of matter combining with form -- this is "substantial change" or "generation of a substance" (e.g. the matter "bronze" combining with form to become the new substance "bronze statue").
- A substance can also come into being as the result of another substance changing its form -- this is "accidental change" or "alteration of a substance" (e.g. the substance "unmusical man" changes to become the substance "musical man").
It's not clear whether Aristotle's own account is entirely coherent, but that seems to be the basic idea.