A few years ago I created an acronym, COW. It stands for "Councilmember from Other Ward".
City councils are like any other legislative body. Certain members are elected by citizens in specific areas. As such, they are those citizens' councilmembers. But, when the council takes action as a legislative body the councilmembers are acting on behalf of the entire city. As such, even a person who lives in let's say Ward II has a definite interest on how a councilmember from, let's say Ward IV votes. Just like somebody from Kansas can be concerned about how a member of Congress from Indiana votes.
And just like with members of congress, the state legislature and other legislative bodies, citizens can express their approval or disapproval regarding certain members of the governing body. And like with other legislative bodies, they cannot vote for or against a member outside of their area, but they can show support for or against them in many legal ways. The most obvious being contributions to campaign funds, for them or against them.
So, get to know who your COWs are. If you like the way they act and vote on items, support them, If you don't like the way they act and vote on items, hold their feet to the fire, even work towards replacing them at the next election.
