The risk of incorrectly rejecting the Null Hypothesis, i.e., rejecting the Null Hypothesis when in fact the Null Hypothesis is true. The probability of a Type I Error for a particular test is called Significance Level (alpha) of the test.
In a criminal court, the possible decisions are to either convict or acquit a defendent. In doing so, two types of errors can be made: convict an innocent person or acquit a criminal. Because of the punishment involved, the first type of error is considered the more serious of the two. There are also two typs of errors in hypothesis testing. Rejecting the null hypothesis when it is true is called 'Type I error' (in general the more serious error) and failing to reject the null hypothesis when the alternative is true is called 'Type II error' (the less serious error).
Type II Error
Type I and Type II Errors on Hyperstat Onlineby David M. Lane - http://davidmlane.com/hyperstat/A18652.html