The formal definition of eScience can be found in the Terms of Reference. A less formal, but more descriptive definition can be found here.
eScience is effective in between the worlds of ICT and e-infrastructures on the one hand and the scientific challenges formulated by academia on the other. eScience workers work closely with scientists, know and understand their vocabulary, help them articulate their questions and challenges in such a way that escience technologies can help them attack those challenges and solve those questions. Formulated in this way, eScience encompasses both the more traditional and the more specific directions. eScience support involves the use of any to all components of the palet of e-infrastructures and ICT-technologies to help scientists do their work properly and efficiently.
eScience is not restricted in its scope of domains and can help in all disciplines and industry and forms a lively community. It develops itself while being applied and strengthens its effectiveness by the continuous exchange of knowledge and experiences gained while working in science projects.
Computational science (scientific computing, scientific computation, sometimes High Performance Computing) is a methodology to solve (often complex) scientific problems, by modeling systems and processes using known physical principles and mathematics and implementing those models in computer programs. The subsequent analysis of the results yield insight in the systems and processes, but also in the capabilities, the limitations and deficiencies of the methodology and of the computer implementation. The optimization of the process: observation, model, implementation, result analysis and comparison with the observation is a typical circle that exemplifies the most important aspects of Computational Science. Because often the real problems are rather complex, the resulting computational problem is ofyter referred to as High Performance Computing. Computational Science differs essentially from Computer Science, which -in very short- deals with the ways computers (and networks) work (best).
Often Computational Science is considered one aspect of eScience. It focusses often on the best implementation of an algorithm on a specific type of computer, although increasingly more often also implementations on grids and clouds are in order.
Data Research is the name of a new direction in science (and industry) and as such comparable with directions named Computational Science and eScience. Both Computational Science and escience deal increasingly more often with Big Data, either in volume, in complexity or otherwise. It is not primarily concerned with efficient storage and retrieval, but more with intelligent analytics, streaming, innovative data base technologies and exchange and with the issues of retrieving information from unstructured data (such as from emails, twitter, facebook or linkedin). Data Research is an example of the topics eScience has to deal with and as such part of the broader eScience domain.