What is the green light on the back of the tower mean and why does it stay on all the time?

In my case it means that it's plugged into the wall.

Probably the ethernet (connection to the internet via cable)

Green light usually indicates that network cable is plugged in and yellow or orange flashing light would mean there is activity. Depends on where the green light is at.

If the light is on the power supply, it indicates the supply is retaining power. Before working inside the computer, it can be used to verify that all power has drained after unplugging the power cord.