An activity is a "distinct, scheduled portion of work performed during the course of a project" according to the PMBOK glossary (5th edition, p. 526).
A key step in managing a project is identifying the activities that must be done in order to successfully complete the objectives of the project. The activities need to be broken apart in a way that supports the scheduling and monitoring of the schedule. This is done in the PMI process of define activities.
Related: activity resource requirements, activity cost estimates, responsibility assignment matrix, planned value, WBS, activity diagram, activity list, activity attributes, decomposition, predecessor, successor, deliverable