Periodically your iPhone will pop up asking if you want to install a Carrier Settings Update. In my book, you should always install these immediately and I’m kind of surprised your iPhone doesn’t install without asking you.
Essentially, a carrier update is a new settings file from your carrier (Verizon, AT&T, T-Mobile, etc.) that instructs your iPhone how to use their services. It contains things like network settings, call settings, what servers to connect to for things like voicemail and picture messages, etc. in order to get the best cellular connection it is important to install these right away.
How long does it take?
Literally seconds. When you tap the “Update” button you iPhone will lose the cellular signal for a brief moment and then reconnect using the new settings.
How do I trigger the update if I previously declined it?
On your device tap the Settings app > General > About. Wait about five seconds. If it is still waiting the message will come back. If the message doesn’t come back you may have already installed it.