Why is there a wave on the water surface when I put something in the water? We've started doing waves in our physics class, but we're doing things very quickly and the teacher doesn't explain anything. And I don't understand why waves work. 
I was thinking that when I fill a bowl with water, and wait until it's still, and then I put a finger in it, then my finger needs some space where the water is, so the water has to move away, like Archimedes said. So some of that water goes up because it's the only place where there's no finger or the rest of the water, and it's easier for the water to push away the air than the finger or the rest of the water. I think it's only the displacement thing that's working here because I tried putting the finger in the water faster, and the effect was pretty much the same except I spilled a lot of water trying different things. 
But I don't get it why after the water has formed this something like a wall around my finger (not that I can see this moment; it's too quick), the wall starts to move towards the rim. Why doesn't the water just flow down the wall, like dry sand flows down a sand wall? Then I think the excess water should spread itself over the surface, but it doesn't do that. So how does this work?
 A: When you first put your finger into the water, the situation is pretty much as you describe; the water is not solid and so the molecules can move, unlike those of your finger or the bowl, so they must move (no two atoms can be in exactly the same place at exactly the same time). Liquids are classically defined as incompressible (technically most liquids including water can be compressed, but the ratio of force to volume is much greater than with a gas), so not only must the water molecules move, they must push all the other water molecules out of the way instead of simply getting closer to them. However, air, a gas, can move and can compress, so initially it is easier for the water to move up against the air than out against more water to get out of the way of your finger.
That's what happens in the first fractions of a second after your finger enters. What happens next involves some very complex math, but the concept is still simple; while water is incompressible, it is still a fluid, and so as gravity pulls on all the water molecules, those molecules move around each other trying to reach a new equilibrium between the force of gravity and the forces exerted by all the other molecules of water. In short, the surface of the water wants to settle down to a new "level". The water that moved up when you inserted your finger now tries to move back down, pulled by gravity. That pushes other water molecules aside, just as your finger did, and with a similar result; some of them find it easier to go up than out. This process repeats itself over time, with the result that a wave of water is generated as water molecules get out of the way of other molecules and then settle. When this wave hits the edges of the bowl, well, that's a solid surface that won't move, so the water can't move out, so it moves up again, and then when it settles there's only one way the water can push and that's back in the opposite direction.
Now, the second law of thermodynamics states that "you can't get the same energy out of a system that you put in"; even at the molecular level, there is "friction", where molecules will simply absorb the energy as heat instead of moving. In addition, as waves bounce around the edges of the bowl, they meet, and when the crest of the wave meets a trough, the two cancel out (the sum of the energies of the peak and trough of a waveform of given amplitude is zero). Eventually, the waves cancel out enough that the water molecules themselves simply absorb the energy and do not move (perceptibly) at all, and the system has then reached its new resting state.
A: I think you are really asking why waves move - i.e. why the waves move away from your finger, as opposed to just staying in one place, or disappearing, or maybe going away and them coming back.
One way to think about it is, imagine holding one end of a long rope.
If you suddenly shake the rope to one side, you start a wave that moves away from you down the rope.
An even more fun example is in a crowd at a sports stadium doing "the wave".
If a bunch of people suddenly stand up, raise their hands, and then sit down,
this prompts the people next to them to do the same - standing up, waving their hands, and sitting down.
However, they cannot do it at exactly the same time as the first people.
They're not that quick.
They do it a little bit later, so the peak of the raised hands moves in one direction, from the first people to the second, and so on, and so on, in that direction.
So why doesn't the second group of people feed back and affect the first?
They do.
The first group of people are in the process of sitting down while the second are standing up.
The first group sees the second group standing up, so the first group slows down its downward motion and settles to a stop in its seat.
(A little far-fetched, I know, but I think it's the right basic idea.)
