From Science Europe Data Glossary

Definition: e-science (or eScience, sometimes also enhanced science) is computationally intensive science that is carried out in highly distributed network environments, or science that uses immense data sets (big data) requiring grid computing.
Alternative definition: e-science is the application of computer technology to the undertaking of modern scientific investigation, including the preparation, experimentation, data collection, results dissemination, and long-term storage and accessibility of all materials generated through the scientific process.
Alternative definition: e-science promotes innovation in collaborative, computationally- or data-intensive research across all disciplines, throughout the research lifecycle".
Explanation: e-science is generally considered to comprise also the humanities and social sciences, which are also separately called e-humanities and e-social science.
References: http://en.wikipedia.org/wiki/E-Science; IEEE International Conference on eScience (2014), see: https://escience-conference.org/