If the p-value is below 0.05 then you can reject the null hypothesis of equal variance at the 5% significance level.
If the test is repeatedly applied to samples from normal populations with equal variances, the p-value would be expected to be below 0.05 about 5% of the time.
A non-significant p-value should not be interpreted as meaning that the variances are equal, only that there is insufficient evidence to reject the null hypothesis that the variances are equal. It's useful to look at the confidence interval for the variance ratio as well as the p-value.
For your last question, I don't know what you mean when you say that the ratio is "mean reverting".