Photography is a science of light. How much light, for how long, and from where, determines the exposure of your image. And exposure is the the base of your image. There are loads and loads of explanations of aperture, shutter speed, and iso and how they affect exposure. I cover Basic Exposure in my post Basic Exposure for Beginners. Here is my take on APERTURE. 
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Aperture is set in f stops. Aperture goes as wide open as 1.2 and as closed 32. The aperture you are able to shoot with will vary depending on the lens. The wider open the aperture, the more light gets in to your camera for the image. Conversely, the smaller the aperture, the less light will get in to your to you sensor. Each FSTOP higher closes the hole smaller and smaller. It can get kind of confusing when starting out, because people may refer to using a "large" aperture meaning they used a small f-stop number which makes for a larger opening. F 1.8, which is the most open setting on my favorite 50mm prime lens, is as large an opening as that lens will open. The graphic above actually starts in the upper left corner with a "higher" or smaller aperture f stop, and ends in the bottom right corner with a "lower" or smaller aperture. 

Aperture basically determines how at what distance your lens will focus and how far it will focus. For example, If you are shooting a your kids in front of the Grand Canyon, you probably want your kids smiling faces in focus and a large portion of the Canyon, too. You want to be able to see where your kids were at the time of the picture. A smaller opening in the aperture  will make for a longer depth of field. And remember, smaller aperture means larger number when changing your settings. 

Lower f stop numbers mean a shorter depth of field. Which in the example above would mean that your kids faces would be in focus, but the background behind them would be more and more blurred the further away they were from the subject.

Below I  have some examples, where the only setting I changed was the aperture or f stop. Notice the subject is the dark duck. I wanted these pictures to have the back lighting so it would stick out how the background was being blurred and sharpened using the aperture. I didn't worry about lighting my subject at this point. 

I shot these with a kit lens 18-55mm becuase I wanted to use a lens that a beginner would most likely have. You can see an even stronger difference with lenses that will open up to larger apertures. All settings stayed the same except adjusting aperture. Notice the stronger difference in the lack of focus of the background from image one, to the more focused back ground of image 6.

You will probably notice, that when the aperture is larger larger, the image lightens. That's because more light is getting in the camera. This is one of the ways you can lighten your image in dark situations, just keep in mind that this blurs objects and scenery that are not the same distance from your camera, because it shortens the depth of field. 
The opposite is also true, by decreasing the size of the aperture, I can decrease  the amount of light on a bright sunny day. However, this would not be the optimum way of doing this by itself if I were taking portraits or wanted a nice bokeh, because it will also bring my my background into clearer focus.

What did you like? What was confusing? What are you ideas? Let me know!

You may be asking "How do I get the right exposure in my pictures? How does exposure work? How does aperture work? How does ISO work? How does Shutter Speed work? What do I do now that I have this big fancy camera? 

Don't worry, I asked the same questions. Everything I know is from trial and error. Lots and lots of errors. I mean LOTS. I watched videos on youtube, read tutorials, pinned 50 blue million tips and tricks on photography. By the way, just pinning them does no good. You kinda have to go read them and put them into practice........
Anyway, I prescribe to the ideology that if you really want to learn you read it/see it, do it. teach it. So let me pass on what I have learned!

Photography is all about light. How much light, for how long, and how sensitive your camera is to that light, determines the exposure of your image. 
How much light is determined by Aperture.
How long the light is allowed in is determined by Shutter Speed.
How sensitive your camera is to light is ISO. 

All three settings can be manipulated depending on the type of picture you are taking. Faster shutter speeds are used for action shots like your son's basketball game. For this picture you probably want to open the aperture for more light and increase your ISO because basketball games are typically inside and the lighting may be poor. However, if you want a little motion blur you may slow your shutter speed just a bit. 

Increasing your ISO can be helpful indoors, or on really dark gloomy days. Just be aware of your camera's limitations. Some entry level DLSR's are quite good at mid range ISO settings. But really high ISO's are normally best left to upgraded models. 

Aperture is also good for increasing or decreasing your exposure. Just be aware of your lens Aperture capabilities,  and pay attention to how much detail you want in your foreground and background. 

The links below will be added as I publish each individual post!