Aperture is one of three elements of the exposure triangle. Not only does it control the exposure, but also lets you control creative effects of an image.
In a nutshell, aperture is the opening inside a lens, which controls the amount of light traveling through the lens to the sensor of the camera. With the aperture control, the exposure of an image and depth of field can be changed directly. However, aperture is more than just an exposure-controlling element since it allows more creative control as well, depending on the lens that is used. Since aperture is hardware-related, the creativity is limited by the lens you use. High-end prime lenses allow broader control in some effects, but you can still get the best out of it even if you have a kit lens.
In this 10-minute video, filmmaker Jeven Dovey explains the basics of aperture and demonstrates the fundamentals of aperture control both for photography and videography. In addition to the basics, he shows how to control the aperture in certain scenarios for getting creative results. He also compares photo lenses and cine lenses in terms of aperture control and shows the differences.