"Stratospheric water" refers to water vapor that is present in the Earth's stratosphere, which is a layer of our atmosphere located above the troposphere. Full definition
Plugging the changes in water vapour into a climate model that looks at the way different substances absorb and emit infrared radiation, they conclude that between 2000 and 2009 a drop in stratospheric water vapour of less than one part per million slowed the rate of warming at the Earth's surface by about 25 %. (economist.com)
In fact, since 1980 (the start of the data analyzed), an overall increase in stratospheric water vapor content as been responsible for perhaps 15 % of the overall temperature increase. (masterresource.org)
Some of the mid-latitude increase of stratospheric water vapor (1 % per year) over the period of 1980 - 2006 can be explained by the increase of atmospheric methane, but not all. (esrl.noaa.gov)