What's a database? We can use pretty much anything as a database, as long as it allows us to store our data and retrieve it later. There are many different kinds of databases. Some allow us to store data and retrieve it years later; others are capable of preserving data only while there is an electricity supply. Some databases are designed for fast searches, others for fast insertions. Some databases are very easy to use, while some are very complicated (you may even have to learn a whole language to know how to operate them). There are also large price differences.
When we choose a database for our application, we first need to define the requirements in detail (this is known as a specification). If the application is for short-term use, we probably aren't going to use an expensive, advanced database. A quick-and-dirty hack may do. If, on the other hand, we design a system for long-term use, it makes sense to take the time to find the ideal database implementation.
Databases can be of two kinds: volatile and non-volatile. These two concepts pretty much relate to the two kinds of computer memory: RAM-style memory, which usually loses all its contents when the electricity supply is cut off; and magnetic (or optical) memory, such as hard disks and compact discs, which can retain the information even without power.