This can mean different things.
If your Green Iguana is basking in the sun, or in a hot enclosure it means that its overheating, and allowing the hot internal air to escape via its mouth. This is natural and not a sure sign of distress, but they need to be able to cool off either via a shady spot within reach or a large water bowl to soak in. Make sure they have access to water if their open mouth continues for a while.
If they are doing this inside an indoor iguana cage, IMMEDIATELY ensure there is cool airflow, and that there is a healthy gradient of temperatures inside. You have a thermometer near their hot basking site, and one in the cooler spots of the cage, right?
Make sure its not hotter than 90 degrees, and that the cool spot is no colder than 60 degrees, no hotter than 75 degrees. If the whole house is very hot, either let them out of the cage or put a fan (safely out of reach!) pointing at part of the cage.
This is a good time to mist them with cool water, and to offer a room temperature bath.
If your iguana is standing erect, and with its tail curled away from you…
Your iguana is not happy and is clearly warning you to back off. It will whip you HARD, or will bite you if your hand gets near. Walk away, stay still and let it see there is no threat, or if you absolutely must grab it, use a thick towel, or a shirt if need be and place it over its head and body, you can then grab it forcefully but gently, wrap it up so it can not bite or scratch you, and then prepare yourself for it to start wiggling like crazy and whipping its tail around.
Keep it close to your chest and bear hug, the tail won’t hurt (much) if its near you. If it does not submit after a minute of wrestling, you have a psychotic Iguana which is not well tamed, and you should put the Iguana in its cage, or temporarily inside a large pillowcase until you can put it somewhere where it can relax and feel no stress. Prolonged STRESS will KILL IGUANAS.