The concept of "aspect" in grammar is quite a tricky one. First of all, aspect is related to grammatical tense, and therefore concerns the verb in a sentence. It basically means "the way in which the carrying out of the action/state is considered by the speaker/writer". In other words: does the action happen all at once, in one go, or more progressively? Is it limited in time, or is it forever happening, or does it repeat itself through time? The speaker’s perspective on how the action unfolds over time is, indeed, what grammarians have called "aspect".
Aspect is, for example, what explains the difference between "I go" and "I am going", so here aspect is expressed through a special grammatical tense in English (present simple vs present progressive). Another aspectual difference is the one between "I went" and "I had gone/been" (past simple versus past perfect). In English, aspect is often expressed through a grammatical structure. In the preceding lessons, most of those aspectual distinctions have been covered in detail, with respect to the differences in the flow of action that they express. However, in certain cases, the same aspectual structures can be used to express a subjective point of view, detached from any idea of temporality – a special perspective either linked to emotionality ("I’m not listening to such nonsense! Won’t you shut up?") or performativity ("please, I’m begging you") or any other form of emphasis or insistence ("I am believing it, yes I do!"). This figurative use depends strongly on situational context. Let’s see how you cope with those subtle nuances!