Database is a set of rows and columns. We use database to store information in it and we can retrieve that information on demand. To manipulate database we use SQL (Structured Query Language.)
There are many database or DBMS (Database Management System) are available few re-known are Oracle, SQL Server, MySql, Sybase etc.
Which database should I choose?
Choosing database is difficult, as all databases perform the basic task of storing database. It depends on your business needs and your budget as, database vary in price and at some point they are different in functionalities also. Before choosing database you should consult with a qualified organisation or individual. You can find differences between databases on internet. It would be worth to look at differences and prices before choosing database.
What are front end and back end?
Front end is UI (User Interface) which you see e.g. any web site is a front end or any application which you see is a front end. Term back end commonly used for database. Data are stored at back end. Those data then cab be representd on Front end which shows meanings to a user.