1.Data that can only take certain values. For example: The number of students in a class. You can't have half a student.
2. Discrete data are vectors or raster data storage systems, which represents objects. A discrete object has known and definable boundaries. It is easy to define precisely where the object begins and where it ends. For example: A lake is a discrete object within the surrounding landscape.
https://www.mathsisfun.com/definitions/discrete-data.html (1.); http://webhelp.esri.com/arcgisdesktop/9.2/index.cfm?TopicName=Discrete_and_continuous_data (2.)