Yesterday we went on a steep hill and suddenly we stopped because the cars in front of us weren't moving..so my mom kept on holding the clutch of the car, then the car started to smoke, maybe it took up to 1 minute before we were in a good position, one guy helped us and he tried to check if the car is overheating but, he said it wasn't and it's fine when we gp back driving in to the highway..the car, seems to be fine, we're still able to get back home, but there's still a little smell of smoke because of earlier. I'm just wondering if the car needs repair and if it's a big deal because the car was smoking earlier? Also if it's good to not use the car or we should often use it after what happened? Did it damage the car?
From this sounds of it, this is typically what is known as "smoking the clutch" ... go figure. This happens when you overheat the clutch/flywheel due to excess slippage. The clutch is one big friction device. There is friction material (not unlike brake pad material) which is suspended between two large, flat pieces of metal. When used normally, there is a small amount of heat generated as the clutch is applied. There is a small amount of slippage, and then the two metal parts grab hold of the friction material and it all becomes like one large mass. At that point no more heat is generated and it starts too cool. When someone is slipping the clutch for a long period of time, the heat continually builds up to the point where the fine particles from the friction material start to burn. This is the smoke you saw. If the slipping continues beyond that, both metal surfaces can become glazed (as well as the friction material) and they will not hold as well. Continue on beyond that and the flywheel can start cracking due to the excess heat.
In your case, if you saw smoke, there is damage. How much damage is unknown without taking things apart. If it is still working, then you may have escaped without too much damage. However, you'll want to be on the lookout for if the clutch starts slipping when you don't want it to. This will usually manifest itself in higher gears. If you find that you press on the gas pedal and the engine increases in speed (tachometer goes up), but the speed really doesn't follow (it should all be very linear), then the clutch is slipping. The other thing to look out for is if the flywheel has heat cracks in it, your take off from a stop may feel more jittery then you are used to. In either case, you're going to want to plan for a clutch replacement sometime in the near future.
I think you're aware of this, but using the clutch to hold the vehicle on the hill is not something which should be done. This is the best/easiest/fastest way to kill your clutch. Use the brakes instead. Not as easy to take off from a stop on a hill, but you'll save your clutch and a large mechanics bill in the process.