So often I see people using their zoom lens to only change angle of view, with little to no consideration for depth of field, perspective and distortion. I see them raise the camera to their eye, turn the zoom ring until their intended subject fills the frame to their liking, then shoot. They are selecting their focal length based on field of view only (or how much you can take in, usually expressed in degrees, like 65 degrees horizontally).
But there are a couple other things to consider when selecting a focal length. A wider lens increases depth of field and wide angle distortion. So when you turn the zoom to go wide, you'll want to think about how that will affect your subject. If you want to shoot a portrait, you'll usually not want to go wide as that can distort peoples' features and eliminate the nice soft blurriness of your background.
Let's take a typical kit zoom lens, like the Nikon 18-55mm or the Canon 18-55mm.
After shooting for a while with a zoom lens like this, you'll want to learn more about focal lengths. Some people will think, hey maybe I should buy a prime lens and shoot with that for a while to learn more. If that's you, then go ahead and buy the excellent Nikon 35mm f/1.8. It's inexpensive, light, fast and ultra sharp. In the Canon system, you can get the 35mm f2. With one of these lenses, you'll learn just what shooting with a normal lens means. Go shoot everything with it. You'll learn that if you need to get closer to your subject, you'll have to use your feet to "zoom" in, and vice versa.
The benefit of a fixed focal length "prime" lens is you'll learn a great deal about that focal length. You'll know how it responds to people subjects, landscape subjects, street photography, whatever you choose to shoot. And importantly, you won't give into the crutch of turning that zoom dial to frame your subject. You'll eventually know even before putting your camera to your eye whether you'll need to step back or step forward to get what you want in the frame.
You'll also benefit from a much faster lens (the prime will gather about 10x more light than your kit zoom). You'll be able to shoot in much lower light conditions without flash, you'll be stunned when you first start shooting with a fast prime.
If you don't want to buy another lens, there is an easy way to simulate the effect of using a prime. Get some duct tape or gaffers tape, set your lens to 35mm, and tape the zoom dial so it doesn't move. Seriously, actually get your camera out and tape it and leave it this way for the next 3 months. Resist the temptation to untape the zoom, as it will impede your learning. You won't get the same shallow depth of field and low light shooting benefits as buying the prime, but you will get a taste of what shooting with a fixed focal length lens feels like.
After 3 months, switch the zoom position to 18mm and shoot everything there for 3 more months. Eventually you'll learn what the different focal lengths will yield.
Below, I've summarized the different focal lengths for you. If you choose the tape method of learning, I would recommend you go in this order: 35mm, then 18mm, then 55mm. The equivalent lengths in full-frame are 50mm, 28mm and 85mm (or the classic lengths for "normal," "wide" and "portrait.")
At 18mm, the full-frame equivalent focal length is about 27mm. This is considered wide angle, and is useful for creative wide angle effects and indoor photography due to the larger angle of view (about 65 degrees horizontally). Wide angle is not traditionally used for portraits due to wide angle distortion (the sides and things closer to the camera get stretched).
At 24mm, the full-frame equivalent is about 35mm. This is considered moderate wide angle or "normal." The angle of view is about 54 degrees horizontally. Neither wide or telephoto, this is a good focal length for street or documentary photography. Great for interior social photography. Not so good for capturing sports from the sidelines (not telephoto enough) or shooting architecture or landscapes (not wide enough). The iPhone camera's angle of view is similar to this focal length.
At 35mm, the full-frame equivalent is about 50mm. This is the classic "normal" lens for full frame film or digital photography. The angle of view is about 39 degrees horizontally. You'll see this length used a lot for a variety of styles including street photography, full length fashion photography or portraiture, still life and product shoots, etc. It's a great focal length due to its relatively low distortion and very "normal" perspective which closely matches the perspective of the human eye.
At 55mm, the full-frame equivalent is about 85mm. This is the classic "portrait" lens in full-frame. The angle of view is about 23 degrees. As the name implies, this focal length is used often for portraits and fashion. The moderate telephoto length minimizes distortion and depth of field, which is flattering for people photography and yields nicely blurred backgrounds.