Levene's test is just a $t$-test of the absolute values of the deviations of the data from their group means. (If you have more than 2 groups, you use the ANOVA; you can also use Brown-Forsythe version of the test, which takes the absolute values of the deviations from the group medians instead.)
At any rate, it is a $t$-test, so the assumptions are based on that. Specifically, you are assuming that the absolute values of the deviations are independent, normally distributed and with equal variances between the groups. It's worth noting that these can't really be quite true. For instance, the normal distribution extends to negative infinity, but absolute values do not. That said, if those assumptions hold for the original data, and your sample size is sufficient, they may be close enough for Levene's test to be reliable.