When we all had film cameras it was a case of selecting your ISO in the shop when you bought your film. You bought ISO 100 film if you thought you'd be shooting in bright daylight, higher for some indoor work. ISO (International Organization for Standardization), despite being a particularly dull and unhelpful acronym, has survived into digital photography.
ISO is the third element of the 'exposure triangle', the three camera settings you can use to adjust the exposure of your images (i.e. how light or dark they are). So your exposure is controlled by your aperture, your shutter speed, and your ISO. Choosing a higher ISO number makes your image brighter, assuming you don't change the aperture or shutter speed.
Changing the ISO setting on your camera is effectively changing the sensitivity of the sensor to light, in a replication of how a film with a higher ISO rating is more sensitive to light. So if you're in dark conditions, can't use a tripod and your widest aperture still means using a shutter speed that's too slow, you can increase your ISO instead.
There is a downside though. For most cameras, ISO 100 or 200 produces the best quality of image. Increasing the ISO gradually increases more noise into the image, especially noticeable in the darker areas of the picture. The quality of image at high ISO settings is however improving all the time with new cameras, so it's impossible to say what is an acceptable maximum. It will vary in each camera, but also depends on your preferences and the type of photography you're doing. It is usually a decision of compromise, whether you want to use a higher ISO, accept a darker image, or choose not to take the photo.
There are a few situations when it is normal to use a relatively high ISO. In sports photography for example, it might be essential to use a fast shutter speed to capture the action. That might mean you need to use a higher ISO setting, especially indoors. Similarly for wildlife photography, especially at dusk or even at night. At very high ISO settings cameras can even pick up details that our eyes can't see.
Learn how to quickly adjust your ISO setting, along with aperture and shutter speed settings, and you've got a good grasp of the fundamental manual controls of your camera. Be gone Auto mode, we don't need you any longer.