This is a pun. "Pouring" is frequently used to describe the state of weather during heavy rainfall, when the precipitation is so strong it is as if water is being poured down from a vessel above. "Poring" is a verb referring to consulting written materials in close detail, as in "poring over her notes". The joke subjects are presumably talking about studying for their upcoming exams. The two words are pronounced the same. The play on words here is that it can refer to either the weather or the exams, and that the joke subjects find either or both to be obnoxious.
When I phoned my friend yesterday we mainly talked about the weather and our upcomimg exams , and we both agreed that the poring was sickening .