If your GEN light is on then the generator votage has reduced down to an extreme low rate or it has died completely, as in, it isn't putting out voltage to recharge the battery.
The gen light stays on when the charging system malfunctions.
It means there's a problem with your charging system.
The GEN light is supposed to light up when the car is started as an indication that the light is functional. If it remains on after the car is started, however, your generator (alternator) is either malfunctioning or not working.
The alternator is under or over charging.
Your "gen" light can be on for a number of reasons. firstly you will have to tell us what make and model car you are referring to, some cars have different wiring so having the gen light could mean any number of things. eg: a blown fuse. Be a little more specific. Also look to see if the gen light is on when you turn the key on but not with the engine going. good luck
The alternator is over/under charging.
Your alternator is not charging or the battery is very low
I have a 76' Malibu and almost the whole time I have had it the gen light is on except when I just put a new alternator in it. Then the light would go out for a while, but always came back on after a while. What I found out was there is a Diode that goes bad in the alternator and causes the light to come on. Soon you have to get a new alternator.
The GED indicator light is an warning indicator. Essentially, it means that the alternator in the vehicle is not charging properly.
Go to auto zone and have the alt checked out. It may not be charging to full capacity.
"Gen" is a shortened form of "generation," often used to refer to a specific group of people born and living around the same time period, such as millennials or Generation Z. It can also be used informally to indicate "general" or "generally" in some contexts.
The prefix gen- means having to do with family or or genetics.