The phrase "to explain the warming" means to give an understanding of the reasons or causes behind an increase in temperature. It involves providing explanations or clarifications about why the Earth is getting warmer. Full definition
These factors, they claim, don't explain the warming of about 0.4 degrees C between 1976 and 1998. (climatesciencewatch.org)
It is very much the mainstream view in the climate research community that you can not explain the warming of the past few decades without anthropogenic and human influences on climate. (discovermagazine.com)
What we are interested in is the longer term less easy to explain warming period from 1920 to about 1950. (realclimate.org)