This arises when multiple looks are taken at the results of experiments. A typical example is that of clinical trials where one looks at the results periodically to see if they have become significant - this is important because the trials are slow and expensive and one would like to stop asap rather than waiting for some pre-determined length of time which might be overkill

The problem that arises generally with multiple testing is that a significant result from a single test is stronger than finding a significant result from many tests (just by chance, one of the many may appear to be significant). So some sort of adjustment needs to be made for that fact that you are taking many bites at the cherry - these are generally called Bonferroni-type adjustments).

What is done is to adjust the significance level (e.g. 5%, 1% known as the alpha-value) at each look in oder to maintain the overall Type-1 Error (a Type I error means the incorrect rejection of a true null hypothesis.)

There are various Alpha spending functions which do this in a systematic way at each interim monitoring point, given the overall alpha. Typically, they establish relatively high alpha-values for early looks, and lower alpha-values for later looks. Thus, they constitute "stopping boundaries," which, when crossed, indicate that statistical significance has been established.

For more info, Google "Alpha spending"