In  geochemistry, paleoclimatology and paleoceanography δO or delta-O-18 is a measure of the deviation in ratio of stable isotopes  oxygen-18 (O) and oxygen-16 (O). 
It is commonly used as a measure of the temperature of precipitation, as a measure of groundwater/mineral interactions, and as an indicator of processes that show isotopic fractionation, like methanogenesis. 
In paleosciences, O:O data from corals, foraminifera and ice cores are used as a proxy for temperature.
It is defined as the deviation in "per mil" (‰, parts per thousand) between a sample and a standard:
where the standard has a known isotopic composition, such as Vienna Standard Mean Ocean Water (VSMOW).   The fractionation can arise from kinetic, equilibrium, or mass-independent fractionation.