A database is a collection of date organized in a particular way. Data bases can be of many types such as Flat File Databases, Relational Databases, and Distributed Databases etc.
A database is a collection of Data. That may sound overly simplistic but it pretty much sums as simple as text file with a list of names. Or it could be as complex as a large, relational database management system, complete with in-built tools to help you maintain the data.