So what exactly do aperture values do other than adjust light intake? I think that ISO values are all about exposure and lower values decrease "noise" what else do they do.
Lets take a step back. The exposure is a result of three things; the aperture (size of the hole in the lens), the shutter speed (length of time) and the ISO (sensitivity). Each of these plays a part and has it's own characteristics.
You can change either of the settings, but keep the same exposure if you compensate by changing the other(s). This is what auto mode and the priority modes do. If you changed one of the settings without changing the others...you would be changing the exposure.
The aperture controls the DOF (depth of field) so you want to use a certain DOF for your shot, you would choose the aperture that gives you that. Then adjust the shutter speed (and maybe ISO) to get the right exposure. This is what aperture priority mode does for you.
Shutter speed controls how motion is recorded...including motion of the camera (camera shake). So to get sharper shots, you usually want longer shutter speeds...and to get blurry shots, you would use a longer shutter speed. In the case of running water, you can blur the water with a long shutter speed but keep the rest sharp by using a tripod an remote/timer.
So to get a longer shutter speed, without affecting the exposure, you could still use aperture priority... just set the smallest aperture (highest F number)...and use the lowest ISO. The camera will then give you the longest shutter speed for a normal exposure, in that light. People often add a neutral density filters, to further slow down the shutter speed.
ISO affects the sensitivity...so with a higher ISO, you would need less light for the exposure. This is good for getting a faster shutter speed...but it also adds noise.