Imagine you have a bag containing 900 black marbles and 100 white, i.e. 10% of the marbles are white. Now imagine you take 1 marble out, look at it and record its colour, take out another, record its colour etc.. and do this 100 times. At the end of this process you will have a number for white marbles which, ideally, we would expect to be 10, i.e. 10% of 100, but in actual fact may be 8, or 13 or whatever simply due to randomness. If you repeat this 100 marble withdrawal experiment many, many times and then plot a histogram of the number of white marbles drawn per experiment, you'll find you will have a Bell Curve centred about 10.
This represents your 10% hypothesis: with any bag containing 1000 marbles of which 10% are white, if you randomly take out 100 marbles you will find 10 white marbles in the selection, give or take 4 or so. The p-value is all about this "give or take 4 or so." Let's say by referring to the Bell Curve created earlier you can determine that less than 5% of the time would you get 5 or fewer white marbles and another < 5% of the time accounts for 15 or more white marbles i.e. > 90% of the time your 100 marble selection will contain between 6 to 14 white marbles inclusive.
Now assuming someone plonks down a bag of 1000 marbles with an unknown number of white marbles in it, we have the tools to answer these questions
i) Are there fewer than 100 white marbles?
ii) Are there more than 100 white marbles?
iii) Does the bag contain 100 white marbles?
Simply take out 100 marbles from the bag and count how many of this sample are white.
a) If there are 6 to 14 whites in the sample you cannot reject the hypothesis that there are 100 white marbles in the bag and the corresponding p-values for 6 through 14 will be > 0.05.
b) If there are 5 or fewer whites in the sample you can reject the hypothesis that there are 100 white marbles in the bag and the corresponding p-values for 5 or fewer will be < 0.05. You would expect the bag to contain < 10% white marbles.
c) If there are 15 or more whites in the sample you can reject the hypothesis that there are 100 white marbles in the bag and the corresponding p-values for 15 or more will be < 0.05. You would expect the bag to contain > 10% white marbles.
In response to Baltimark's comment
Given the example above, there is an approximately:-
4.8% chance of getter 5 white balls or fewer
1.85% chance of 4 or fewer
0.55% chance of 3 or fewer
0.1% chance of 2 or fewer
6.25% chance of 15 or more
3.25% chance of 16 or more
1.5% chance of 17 or more
0.65% chance of 18 or more
0.25% chance of 19 or more
0.1% chance of 20 or more
0.05% chance of 21 or more
These numbers were estimated from an empirical distribution generated by a simple Monte Carlo routine run in R and the resultant quantiles of the sampling distribution.
For the purposes of answering the original question, suppose you draw 5 white balls, there is only an approximate 4.8% chance that if the 1000 marble bag really does contain 10% white balls you would pull out only 5 whites in a sample of 100. This equates to a p value < 0.05. You now have to choose between
i) There really are 10% white balls in the bag and I have just been "unlucky" to draw so few
ii) I have drawn so few white balls that there can't really be 10% white balls (reject the hypothesis of 10% white balls)