Welcome to the forums. You will find that photography is a series of compromises. It is similar to playing "wack a mole". You push the high point down here and something pops up somewhere else.
So, ISO speed. Probably the best way to understand it is to look at the results. See the link below
ISO Comparison
You can see that the images go from 100 to 3200 and at 3200 the images look pretty gritty or grainy or noisy. Now I figure you have a couple of questions -
Why does it look this way? - The camera's sensor is a grid of points that captures the light. The higher the ISO the more sensitive the points become. At the higher end, say 3200 they get so sensitive, that when they get hit with a lot of light, the points become so excited that they affect their immediate neighbors, so some of this excitement spills over to the other pixels and this excitement also gets recorded. This is noise, and it creates the graininess that you see in the picture. There are utilities that you can use to remove a lot of the noise in post processing.
You have to understand that ISO speed is just one of several parameters or controls the photographer has over taking the image. So lets follow the light into the sensor. First there is the lens, then the aperture, then the shutter, and last the sensor.
Lens - the lens collects the light and focuses it. It has a mechanism within it that adjusts the amount of light that is let through. The mechanism is called the aperture. Lenses that are able to collect a lot of light, are made of very high quality glass, and thus are very expensive. The more light they collect and able to transmit to the sensor, the "faster" the lens is. The lens is labeled by its focal length and its best aperture. e.g., 50mm (focal length) f1.7 (largest aperture)
Aperture - The Aperture is the size of the hole that is adjustable that lets a quantity of light through. This is similar to you squinting in very bright sunlight - you narrow down your eye's aperture so that you can see better. The size of the hole is numbered by an f number and called a stop or f stop. The large hole has the smallest number, i.e., f2.8 or f4. The smallest hole has the largest number, f22 or so.
Shutter - The shutter is in the camera and is a curtain that covers the sensor. This is pulled up for a period of time. The longer the sensor is exposed, the more light is collected by the sensor. Shutter values range from about 1/4000 of a second to 30 seconds.
Sensor - As indicated above this sets the sensor's sensitivity. The higher the number the more sensitive it is, but the more graininess there is recorded in the picture.
Now all of these numbers have relationships among each other. Making the aperture hole larger, you can cut down on the shutter time OR the ISO speed, or a combination of the two.
You can have a high ISO speed (3200) - but that usually results in grainy pictures
You can have a long shutter speed (1 second), but if you do not shake the camera, the object in the picture may move - and you get a blur, or too much light and resulting in just a white image.
Putting the camera in the green mode - the computer figures out everything, sets up the camera, and you take a pretty good picture.
So why do folks want to override the camera's computer to take pictures. Well to come up with different types of images. So lets say you want to take a night picture of the highway getting streams of tail lights from cars moving down the highway - Well say you want a good quality picture, so use an ISO of say 800 or less. Then you can experiment with the shutter speed to get the desired amount of tail light streaking. The longer the shutter speed the more streaking effect.
hope that helps ...