As Apple describes it on its support site, "Carrier settings updates are small files that can include updates from Apple and your carrier to carrier-related settings, such as network, calling, cellular data, messaging, personal hotspot, and voicemail settings."
In other words, they handle anything related to how your device connects and communicates to your carrier's network and any related services.
The updates are largely used to add new features or enhance the performance. This can include adding support for upgrades made to a carrier's network or the rollout of new functionality like voice-over-LTE, which promises to deliver better-sounding voice calls.
Updates can also be used to fix a problem. For example, a carrier update was issued after a bug was found on the Verizon iPhone 5s that was causing the phone to use cellular data while connected to a Wi-Fi network.
Another instance where a carrier settings update may occur is when you swap out SIM cards. Let's say you've been using an unlocked iPhone on AT&T's network and decide to switch over to T-Mobile. Your iPhone will need to update its carrier settings so the device can work with the new provider. The same is true if you travel overseas and want to use a local SIM card to save money.
The update may happen automatically once you insert the new SIM card. But if not, you can go to Settings > General > About to start the process manually.
Since these updates tend to be smaller in size than major system upgrades, the update process should be faster, so you don't have to be offline for very long.