This is the literal translation of the English term climate change. However, it is rarely used in Tagalog/Filipino language since the English term is more widespread in the Philippines.
Pagbabago means change, alteration or transition. The term klima is used for climate but can also mean weather or season. There is another Tagalog term, panahon, that is used for weather or season. However, panahon can also mean (a period of) time in the sense of an occasion, era or epoch. It's like in the Spanish term tiempo that can mean both time and weather as well.
It that sense, the understanding of climate change as expressed in the local term pagbabago ng klima is that of changing weather patterns or strange seasonal variations, like rain in dry season.