The wide-angle lens gives you a significantly wider angle-of-view. This means that if you keep your camera in one place and take two pictures, one with the wide-angle lens and one without it, the picture taken with the wide-angle lens will include parts of the scene that were outside of the frame of the picture taken without the wide-angle lens. Another way to say this is that the wide-angle lens will give you a more “zoomed-out” view.
Depending on what you are photographing, this effect may be more or less obvious. If, for example, you are at a restaurant with a group of friends and want to take a picture without leaving your seat, the difference provided by the wide-angle lens will be very noticeable because you will be able to include more people and more of the table in your photo. However, if you are taking a photo of trees outside, you may not notice as much of a difference because how much of a repeating pattern like leaves and branches are included are not as obvious to our eyes as how many faces are in a picture. Also, in that scenario, it would be easier to position your camera farther from the tree to include more of it in the picture, which would have a similar effect to using the wide-angle lens.
Galen Michel