Point of confusion: Alpha with Bonferroni correction.

 Statistical Significance is defined simply. When a P value is less than a preset threshold, called alpha, then the result is deemed "statistically significant". 

But what about when you make several comparisons at once? What happens to alpha?

The simplest correction for multiple comparisons is the Bonferroni correction. The threshold for significance is reduced to alpha/K, where K is the number of comparisons you are making. So if you are making three comparisons, the threshold for significance is 0.05/3 = 0.017. 

Alpha is still 0.05. The key point is that now this significance level applies to the entire family of comparisons, not to each individual comparison. The threshold used for each individual comparison is alpha/k.