To explain what L, 1 and 2 stand for I will need to refresh our memory on the main difference between a manual transmission car and an automatic transmission car. That main difference is that the automatic transmission car shifts between gears automatically while the manual transmission car requires that you do the gear shifting yourself.
And why does the car require gear shifting, whether automatic or manual? Here's the stripped down technical explanation. The engine of your car has to convert the fuel its burning into a rotational movement that ultimately drives your car forward. Gears are needed for this. One gear could have been enough. The gear will help you move your car in the morning from where you've parked it and keep you going till you get to your destination. If we were to give the gear a number, it would be called gear 1. However, the trouble with this is that your car require a lot of energy to move from a stopped position to a moving state. The same way it's harder to push a car that suddenly stopped at the middle of the road from it's stopped state, even if you are all 3, than to join the two others while the car is already being pushed into motion. You will all put in the most energy at the start of the push than while the car is already gliding slowly down the road. So the gear 1 would be made in such a way that it would be able to provide that lots of energy required to move your car from stopped state.
According to the laws of Physics that govern this engine to gear power transmission, the more force rotation (torque) you give the less speed you get. The gear 1 would require high torque in other to help start your car so you are severely limited speed wise. And this is why you've got other gears, gears that can now take over after you've gotten the car started and need more speed. So now you know why you have other gears. And it's same whether your car is automatic or manual.
Back to our original topic: 1, 2 and L in the automatic transmission car. The "what" is simple, it's the "why" that is quite tricky. 1 stands for gear 1. L also stands for gear 1. 2 stands for gears 1 and 2.
When you put the automatic car in 1 or L, you are forcing it to not change to other gears but use gear 1 only. The benefit of this is that you will get the highest torque your car can produce. This could be beneficial if your car is stuck in mud and need the most torque not speed. While putting your car in 2 forces the car to only shift between gears 1 and 2. The logic is same as for 1, you need more torque than speed. A practical need is if you are dragging/towing your friend's big car up a hill. The danger in using these positions is that if you get back on the usual road and starts hitting hard on the accelerator to move at the speed the other cars are going then you are on course to killing your car engine. Your car engine will keep rotating really fast and if you take a look at the tachometer (that speedometer-like stuff on your dashboard that read RPMs) the pointer will be at the red part and we all know that red signifies danger. But you still wouldn't gain the speed you desire because you have selected high torque low speed gears, and you will keep revving up the car thinking the speed will increase, till you damage the engine and the car stops.
Now you know why it's a good thing that you've not been using them.