Comment by DaCapoo

Typically, when you open a secure shell (SSH) connection your client is connecting to a SSH server running on the target machine. A reverse shell occurs when the server initiates a connection with a client that is listening - for example, you have access to a shell to run commands on a target computer (usually through a command injection vulnerability in a website). This means you don't have a full shell - just the ability to run arbitrary commands.

You open a reverse shell which instructs your target computer which is running a SSH server to connect to your client, which allows you to now have a full featured shell at your hands.