Great question! I will do my best to answer what natural selection is.
First, what is selection? This might sound simple (selection is, well, selecting) but it really isn't. In a biological sense it is selecting those characteristics that are best able to survive given the current circumstances. I apologize for the lengthy example but I hope it illustrates my point. Please bear with me on this!
Here is a real world example. Dandelions are common weeds in lawns. If you look at a field of dandelions you can see that they are not all the same. Some are very tall, some are short. Some have leaves that stick up, some have leaves that are flat against the ground. This is natural variability that exists in the dandelion population. If you look at alot of dandelions you may find actual mutations, some with curly leaves, etc.
If you then examine dandelions in a regularlly mowed lawn you find only those that are flat leaved (leaves are level with the ground) and the flowers are on tiny, short stalks. As a scientist you might wonder why are the dandelions this way in the lawn when the ones near the fence or outside the lawn are different (as in normal tall, short, a mixed population).
In science when we observe something we don't understand we form hypotheses. These are ideas that may explain what we see. What makes a hypothesis unique is that it is framed in a way that we can test. Usually a scientist will try to think of all possible explanations that would lead to what is observed. For our dandelion example you might think of these:
1) Dandelions have a means of recognizing a mowed lawn and only produce short offspring in this situation (they only grow as tall as the surrounding vegetation)
2) Dandelions that have been mowed down change their breeding strategy so that future offspring are short (they can adapt to environmental changes)
3) Tall dandelions and their genes became extinct in the lawn because only short ones survived the mowing
After outlining these ideas as a scientist you would then think of experiments to test them. You are not trying to prove them, you are trying to disprove them.
So for #1 you might transplant dandelions (or plant seeds) from the lawn to an unmowed habitat. If the plants or offspring grow tall then you didn't PROVE #1 but you did fail to disprove it. As it turns out the offspring are just as short as their parents in the lawn, so you now reject #1.
For #2 you might do a repeat experiment. Plant your mowed dandelions in an unmowed field and see their height. You also might take an tall dandelion crop and mow it to see if the next crop are short. As it turns out the mowed dandelions produce short offspring and the tall ones continue to produce tall offspring, no matter how many generations you mow them.
For #3 you could take seeds from your lawn samples and seeds from your unmowed samples and grow them in an experimental plot. If they both grow tall (or short), then you disprove #3. If the tall seeds grow tall and your lawn seeds are short, then you again failed to disprove #3. As it turns out this is the result that is seen.
Now in your dandelion experiment you have the following results:
#1 - unlikely
#2 - unlikely
#3 - not disproven
Because #3 is not disproven you might think of other experiments to test it further. But in this case let's pretend this is the end and you go with number 3 as the answer to the big question, "why are dandelions in mowed lawns short?".
Your experiment demonstrates selection. Only those dandelions that carried the genes for flat leaves and short flowers survived to reproduce. Out of the millions of dandelion seeds that blew into the lawn, only the shortest were able to have offspring in that environment (remember, the ones nearby were tall and normal). If someday the house went unsold and no one took care of the lawn anymore this could change. The grass could grow and shade the short dandelions. Only those mutants in the 'short' gene pool that were slightly taller could survive to reproduce. Eventually their descendents would look very much like the original types, tall and with upright leaves.
This is natural selection, even though it is a human-caused environment. In place of dandelions think of deer with thick and thin coats living in a valley. If the climate changes to cooler those with thicker coats may have an advantage. They have more offspring and soon the whole population carries the gene for thick coats.
The important point to keep in mind is that selection is ONLY for the current environmental conditions. And several different traits may be selected for at the same time, sometimes in different directions. This is why we see variation in selected traits.
I again apologize for the length of this post, please feel free to ask questions. -LM