Aperture is just a fancy name for a hole, and I'm guessing that early photographers thought it rude to shout "how big's your hole" so Aperture it is. Then, for some reason, it was decided that the smaller the hole, the larger the designated number. Your guess is as good as mine on that one.
There is, of course, a geeky answer to this, f being focal length, divided by aperture diameter gives fstop or something like that. Yeah, I know, my eyes glazed over too. But if you are interested, look it up, I'm sure you'll have hours of fun.

But for me, it's a simple question of what role does it play in the exposure triangle and what differences does it make to my photographs?

The aperture controls two things in essence. The amount of light entering the camera and hitting the sensor, and the depth of field.

Depth of field. That's another one; it should really be "depth of in focus" to make real sense. The depth of field is simply the amount of the photograph that is in focus from a given point to another given point. A shallow depth of field would be used in something like a portrait where the subject is in focus but the background out of focus, giving emphasis to the person being photographed. Say f2.8. A large depth of field would be when you want everything in focus, say in a landscape photograph. Say f16.
we shall, of course, go more into the depth of field 

So how is this used?
If your need is to use the shutter speed as your priority, for sport (faster shutter speed required) or for a long exposure shot for the arty farty look, then aperture will be used as an amount of light let in tool or as the depth of focus tool.

Its one of those things with photography, at first they are hard to understand as a single entity, but once they start to be put together, they start to make sense.

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