Whenever such a request pops up, you can simply tap it to open a view detailing the objective. Typically such requests will ask you to provide a specific need to a building already in place. From there you have 2 options: dismiss it (and the request will disappear), or accept it.
If you accept a need request, you will be brought to need finder menu to view which buildings can help you fulfill the request. The request bubble will remain if you exit the need finder menu. You can fulfill the request at any time, it’s really up to you.
You might also be asked to upgrade a property. If you accept the request, you'll be taken directly to the auction house to look for the property in question. The request bubble will remain if you exit the auction house.