Alignment is the equivalent of game karma or perhaps your reputation as a ruler.

Low alignment has a negative impact on immigration to your colonies and as such the growth of your empire. It will also make you a less desirable employer for scientists, with less applying to work for you and some in your service possibly even leaving.

Being a benevolent ruler and keeping your citizens happy and healthy increases your alignment over time. Hostile actions reduce it, depending on who and what you target. Minor skirmishes among enemies have little effect, at the other end of the spectrum would be to raid a friend's colony.