Action started in past, it was a continuous activity until it just stopped (or action stopped recently)
we have a connection between this recently stopped activity and the present situation at the moment of speaking (has a result now).
You look sleepy. Have you been reading? (you started reading some time in the past, you recently stopped reading and you look sleepy = result now, at the moment somebody is speaking this sentence)
Now let me talk about this so called connection with the present. This connection means present “result” of the activity which started in the past and stopped recently. As you can see, perfect line of tenses loves this “result” concept. You look sleepy = connection with the present or present result at the moment of speaking.
The ground is wet . It has been raining.
In the above example it’s not raining at the moment of speaking. However, it started raining some time ago, continued to rain, and stopped recently (or a moment ago). And we have a present result “the ground is wet”
Another way to explain this present connection or result is when an action isn’t ongoing anymore, but the evidence continues to be. It looks like the evidence prolongs the complete action and, sort of, makes it “still ongoing.” Personally, I think this is the reason why we use the verb in the “continuous” form (ing), even the action is complete (perfect means complete). Also, It could be the reason, or one of the reasons, why present perfect continuous has this particular use.
Some additional ideas on the Present Perfect Continuous regarding this particular use
A complete (perfect) action, the evidence of which continues (continuous) to live in the present = The Present Perfect Continuous Tense.
However, let me analyze the name of this verb tense in connection with the formation using this example.
Present (it has (not had)) Perfect (the activity is compete – been) Continuous (raining) = we have a completed continuous activity.
We can also think of it this way:
We have just had a lasting activity, and the evidence is still present (continues).
More on Present Perfect Continuous Tense: