This tutorial explains the concepts of hypothesis testing in statistics.
Hypothesis Testing
Many text book uses the court case example to explain hypothesis testing. In the U.S. (but not all countries), the court finds evidence to prove the defendant guilty, instead of proving the defendant innocent.
There are two hypothesis for a court case:

The defendant is guilty – when we have a theory and try to prove it, the hypothesis is called H1

The defendant is innocent – the alternative of H1 (you can simply interpret as something is normally true, i.e. everyone should be innocent) , the hypothesis is called H0 (Null hypothesis)
We don’t prove someone is innocent because we have assumed so, we just need to see if there is enough evidence to prove the defendant guilty.
If there is enough evidence, we say: There is enough evidence to conclude that the defendant is guilty
If there is not enough evidence, we say: There is not enough evidence to conclude that the defendant is guilty, but we cannot say the person is innocent
Hypothesis Testing Errors
As we try to prove defendant is guilty, an innocent person may be judged guilty (which is very serious) or a guilty person is judged innocent. Using the statistics terminology to describe these two errors:

Type I Error / False Positive (probability is α): We found enough evidence to conclude the defendant is guilty, but it turns out the person is innocent. α is the level of significance we allow to reject null hypothesis.

Type II Error / False Negative (probability is β): We could not find enough evidence to conclude the defendant is guilty, but it turns out the person is guilty
Examples of Hypothesis Testing
Given μ = 100, if we try to prove population mean >100, then
H0: μ = 100
H1: μ < 100
If we try to prove population mean ≠100, then
H0: μ = 100
H1: μ ≠100
Outbound References
http://www.sagepub.com/sites/default/files/upmbinaries/40007_Chapter8.pdf