The Generator is the facility on the Helicarrier responsable for producing and storing Credits. It produces 20 credits per hour. Clicking on the Generator will collect all credits stored on it. When the green bar over the Generator is full it can no longer store any more Credits.
The Generator can be upgraded on the Research Lab to increase the Bank cap (the amount of Credits your Generator can hold) and the Max credits which are shown on the top right of the main screen.
Upgrading the Generator is important when you want to research something that requires more Credits than your current Max credits allows you to hold.