Vabsie,
The most dangerous component in the airplane continues to remain the pilot.
Engine failures can occur from environmental conditions (carburetor ice, for example), misfueling (contaminated fuel, water in the fuel tank, etc), mechanical problems (thrown rod, slipped magneto, failed valve...) or disruptionto airflow (blocked air filter, and so forth). Regardless of the cause, and regardless of the statistical frequency at which they may occur, one always plans for them and takes full advantage when it doesn't happen.
I once experienced a very rapid onset of carburetor ice in a straight-tail Cessna 182 in instrument conditions. The engine ran rough and as I pulled the carburetor heat on, the control broke off in my hand (the wire leading to the carb air box failed). I landed on a gravel strip in a valley after emerging from the base of the clouds. It was a high base, and the landing was uneventful. On another occasion I pushed the power up too quickly when deer ran in front of the J-3 cub I was flying, and the engine promptly quit. I was attempting to go around, but made other plans one the power was gone. That too, was uneventful. On another occasion, I experienced a rough engine and then a failure due to a fuel flow fluctuation condition in a Cessna 207. It was in rough desert mountain terrain, and I was close to the terrain. It happened to occur in an unfavorable spot. Switching tanks, applying boost, and adjusting the throttle and mixture resulted in a quick recovery and an uneventful landing at an airport not long thereafter.
On another occasion in a Cessna 206 a lot of banging and vibration occured when a magneto failed not long after departure. I prepared to land on a road, and in the process switched mags, found that it ran extremely rough on one and very well on the other, and made an uneventful landing at an airport not too far away. On another occasion with a student, the airplane began vibrating hard and shaking, I reduced power and remained over a highway while making my way to an airport. I continued to climb a little as I went, and kept suitable sites to make a forced landing beneath me. I landed at the airport without event. On another occasion with a student, following a simulated power off approach to a runway during training, the student applied power to go around and we did...for about 30 seconds...then the engine ran very rough and then quit. Timely application of carburetor heat restored power and we continued around the pattern.
You can see a pattern. How the event ends is largely under your control, and that's why you're doing your training. It's all part of the preparation to be the pilot in command of your airplane. It seems a scary thought presently, perhaps even daunting. It's not. If your instructor is worth his weight in salt, then by the time you're done, you'll be pleasantly surprised when your your engine doesn't fail, and an engine failure should be a second-nature occurence.
I was behind an Ag Truck as we prepared to go spray a field about 20 years ago. I saw a very bright fireball come out of his airplane as the exhaust blew off, a brief explosion, and he shut down. The damage was minimal, and the cause was a failed magneto. It had disintegrated, in fact. It happened on the ground as he advanced power to move onto the runway. Furtunately it happened then, but he was as fully prepared as I was to deal with it had it happened during the takeoff or any time thereafter. Just as you will be.
Bob Hoover, a well known aerobatic, test, and combat pilot, used to do an airshow routine in a shrike commander. It involved a full aerobatic demonstration on both engines. Then he would shut down one engine and perform the routine, then shut down the second engine and perform it without power. It's a matter of energy management and airmanship, and he did a superb job. The mere fact that he had no power available didn't hinder his ability to control the airplane. In fact, part of his routine was returning the airplane to it's starting point after the power off routine...still without power.
Losing your engine can and does happen, but it's not a dire emergency unless you make it so. After you've been training for a short while, you'll see why. The glide down, and the distance it consumes, is really significant only in allowing you to reach a suitable landing site. The ability to glide a long distance is meaningless and irrelevant, if you always keep an engine failure in mind, act accordingly, and keep a suitable landing site nearby. Do that, and you needn't fear.
There are few things more pleasurable than flight in a light single engine airplane. Enjoy every moment of it. Should the occasion arise when you have an opportunity to to exercise some of the abnormal or "emergency" skills you'll learn, be grateful for the experience and savor it. Such occasions don't come along often, and can't be bought with money. Fly safe.