From Science Europe Data Glossary

Definition: e-infrastructure is a technological and organisational arrangement of computing software and hardware that provides researchers with benefits including shared access to large data collections, advanced ICT tools for data analysis, large-scale computing resources, and high-performance visualisation.
Explanation: it embraces networks, grids, data centres and collaborative environments, and can include supporting operations centres, service registries, single sign-on, certificate authorities, training and help-desk services. Most importantly, it is the integration of these that defines e-Infrastructure.
Reference: http://www.jisc.ac.uk/media/documents/publications/einfrastructure_rtf.rtf
See also: data infrastructure; research infrastructure