"Sister" alliances just means the two groups work as a team in war... so if you declare on Alliance A, and they are sister to Alliance B, expect Alliance B to declare on you.

They are not (or should not be) run by the same person via multi-accounting (which is not just against the rules, but a bannable offense that could cost you both accounts).

Often, when an alliance is full, or has a lot of low-prestige players, they will appoint one of the officers to open a sister alliance either to take the overflow or as a training alliance for lower-level players to build up their skills and armies. In this way, those weaker players can count on learning the game from experienced officers, and having a bit of extra protection from the experienced players in their sister alliance if a high-level player starts trying to farm them.