The phrase "decade warming" refers to the gradual increase in temperatures that occurs over a period of ten years. It means that the Earth is getting hotter year after year for a whole decade. Full definition
From year to year the global average temperature can increase or decrease, but over decades the warming trend is clear. (earthjournalism.net)
The link is to their news story of the release, which they title «Past Decade Warmest on Record According to Scientists in 48 Countries». (skepticalscience.com)
They found that volcanic activity, as measured by aerosol optical thickness data (AOD) has only caused between 0.02 and 0.04 °C per decade warming from 1979 through 2010 (Table 1, Figure 2), or about 0.06 to 0.12 °C warming of the surface and lower troposphere, repsectively, since 1979 (out of approximately 0.5 °C observed surface warming). (skepticalscience.com)