What does Posterior tail-area probability mean in Causal Impact?

I'm new to CausalImpact package in R. I'm trying to understand what the p-value or Posterior tail-area probability mean in the summary. Does it mean that because the p-value is very low, the chance that there's an effect of an intervention is significant? How to put it better in layman's term?

In the example (to be run with example("CausalImpact") in R), the summary shows a positive effect and reports a tail-area probability of 0.001. This means: if the intervention had no effect on the response variable, there would be a chance of only 0.1% to see a positive effect at least as large as the one observed.