What does "the intercept being statistically significant" mean?

You can safely ignore that information.

Statistical test is a test of whether a coefficient is different from zero, so in the most general context, the intercept being different zero doesn’t have much meaning in and of itself. We can force it to mean something, though. If a) we standardize the outcome score such that the average is 0 (In SAS, this would be proc standard mean=0; var outcome;run;) and b) if the intercept is significant, it means that whatever the intercept represents (e.g., Hispanic student’s average score) is significantly different from the average score (I'm using "significantly different" in a sloppy way to focus on the main point of my explanation).

Having said that, I just made this up just as an example. Generally speaking, we should ignore the intercept’s significant level.

In contrast, the intervention effect being significant means something important and often exciting. If the intervention effect is .20, statistical test examines whether .20 is different from 0. 0 means no effect, so if the impact coefficient is statistically different from 0, it's a good news (you would also want to examine the size of the coefficient too.)