Simply put, the shell is a program that takes your commands from the keyboard and gives them to the operating system to perform. In the old days, it was the only user interface available on a Unix computer. Nowadays, we have graphical user interfaces (GUIs) in addition to command line interfaces (CLIs) such as the shell.
On most Linux systems a program called bash (which stands for Bourne Again SHell, an enhanced version of the original Bourne shell program, sh, written by Steve Bourne) acts as the shell program. There are several additional shell programs available on a typical Linux system. These include:ksh, tcsh and zsh.