The simplest definition of Analytics is "the science of analysis". In reality, the word "Analytics" has not been properly defined by the professional community and may mean different things to different people. A simple and practical definition, however, would be how an entity(i.e., business) arrives at the most optimal or realistic decision from a variety of available options, based on existing data. Business managers may choose to make decisions based on past experiences or rule of thumb, or there might be other qualitative aspects to decision making; but unless there is data involved in the process, it would be considered beyond the purview of analytics. Another definition could be that Analytics is a field of study / profession that has applications in any field (business / social / political / home) where data is available.
Common applications of Analytics include the study of business data using statistical analysis in order to discover and understand historical patterns with an eye to predicting and improving business performance in the future.