Aperture is the factor that determines how much light is let through your lens and on to your camera’s sensor.
This can be compared to the human eye. When you walk into a dark room, the iris in your eye opens up to allow more light in so you can see. When the lights turn on in the room, the iris closes to reduce the amount of light going through the iris.
With a lower aperture setting (i.e. f1.8), your subject will be in focus with a blurred background. This is desirable for portraits.
When the aperture is raised (i.e. f16) both the foreground and background of your image will be in focus. This is desirable for landscapes.
Aperture is directly tied to shutter speed. In a situation where you are shooting in daylight, a lower aperture will generally mean a higher shutter speed as the light landing on the sensor needs to be controlled. If you put your camera in to the “A” (Aperture priority mode) you will notice that the lower you adjust the aperture the higher the shutter speed goes.
The camera automatically does this to compensate for the amount of light landing on the camera sensor. If you were to use a low aperture with a low shutter speed, your images would always be overexposed.
Shutter speed is how fast the shutter is actually moving. If you are using a high shutter speed, you can completely freeze motion. See the image below for an example:
Higher shutter speeds are generally used for action shots or to compensate for low apertures in bright light. Higher shutter speeds also give sharper images as everything becomes frozen and there is no chance of a blur.