Hey, planrforrobert, I can't send an IM consisting of more than 2500 characters or whatever, so I'll just cut-&-paste into here.
Hm... the easiest way that I can understand it is this. Exposure refers to many different things. Exposure can mean how long you leave the shutter open to get the picture. Each picture you get is also referred to as an exposure.
Actually, that's all a bit confusing, because we use the word exposure to mean many different things. Basically, three factors will affect your pictures.
1. Shutter Speed
If you shot with film back in the day, you should remember loading particular films for particular situations. Like ASA 100 for sunny days, and ASA 400 for overcast days, etc, etc, etc. If you didn't shoot with film, or are too young to remember it. Just realize that digital ISO was built to mimic and be equivalent to film ISOs. ISO refers to film sensitivity. Meaning, back in the day, there was little pieces of silver something-or-other that would catch the light. The MORE silver you had, the quicker you could expose the shot to get the picture you wanted. So, basically think of it in this way. If you are building a house, having more builders working on that house at the same time, means the house will be built in less time, right? So, basically, if I have 100 people building my house, it would take longer than say 400 or 1600 builders. So, this metaphor is like our photographs. ISO refers to how sensitive our sensors are to light, meaning we can capture the picture we want in shorter or longer periods of time depending on ISO.
The next question would be, then WHY do we not want to shoot with 1600 ISO at all times then. We would get the pictures in less time, and quicker is always better, right??? Well, no, not exactly.
The thing that we need to realize is this. Here comes another metaphor. Remember that example I gave you regarding building homes? So, we have 100 builders building our house. The thing is that as soon as we build the house, those 100 builders are going to move in with us into that house. Same with the 400 and the 1600. Think of how crowded your house will be with 1600 builders in it? Pretty crowded, right? Same with our photos. The higher the ISO, the more grain and noise we get. And noise can ultimately detract from our shot. So, basically, you want to shoot with as low ISO as you can for the given situation.
Exposure is a calculation of those 3 factors I told you earlier: SS, F/Stop, and ISO.
So, for example, let's say for a shot that we want to take. The settings for a "properly" exposed shot is this:
Shutter Speed = 1/100th of a second
Aperture = F/4
ISO = 100
By turning up the ISO, it means that we can change the shutter speed or the aperture, or possibly a combination of the two and result in the same "expsoure". Does that make sense?? If you take one away, you need to add to one of the others to get the same "exposure."
So, in that example, if we changed the ISO to 200, we might be able to shoot at a higher SS while staying at the same F/stop to get the "proper" exposure.
So, that's basically it. Changing your film sensitivity allows you to shoot higher shutter speeds, or narrower f/stops (i.e. - higher number) while keeping the same exposure.
Kinda long, but hope this helps. If you don't understand that. I would recommend that you look up "Exposure Pyramid" or "Exposure Triangle" and google it to see what that yields for you.
Best of luck,