Consider two sentences:
I know about usage of simple past and present perfect, but these kinds of sentences baffle me. What essentially is different between above two?
I really have a problem with present perfect in some sentences.
The difference here is slight. It depends more on context than the difference between present perfect and simple past tense.
The simple past tense (example 1) is used to refer to an event that was completed in the past. When in the past is not specified: it could be long ago ("The dinosaurs lived at least 65 million years ago") or recent ("I typed the previous example").
The present perfect tense (example 2) is used to emphasize the importance of a completed event in the present. As Wikipedia explains, present perfect tense expresses "a past event that has present consequences." In other words, the perfect aspect emphasizes the result over the occurrence in some way. It is often used in conversation or other personal forms of contact, where what I have done likely matters to whomever I'm addressing.
That slight added emphasis or aspect doesn't do much in this example because the context does more to determine how the event described by the verb is understood. Let's assume this is taking place during a conversation where you didn't understand something the other person said. Example 2 ("I don't understand a word you have said") could encompass the entire conversation, the last utterance, or even a single word. The tense and aspect express the utterance's relation to your present moment of confusion. Example 1 ("I don't understand a word you said") doesn't even define that much grammatically. You said something in the past, and I don't understand it now. It's only logic and context that determine what in your previous utterance I'm referring to, and in most cases that would be enough.
The present perfect would matter more if I need to emphasize that I completed a task to someone who cares about it. So if I had to pay rent and was talking to the landlord on the day rent is due, I might assure them: "I have paid the rent," or "I've already sent the check." If I were focused more on it as an event in the past, like in writing my own journal, I'd more likely write, "I paid the rent" or "I sent the check today." I could use the simple past with my landlord too ("I paid the rent"), but it would come across as plainer or more familiar without the perfect aspect.
