Airplane mode is primarily designed for, as the name implies, use on an airplane. It temporarily disables wireless transmission, including your cellular connection, Wi-Fi and Bluetooth, as well as notifications and any other online content. The purpose is to comply with airline regulations while you're in flight. But the feature can also be used to shut down your phone's communications without turning it off when you don't want to be disturbed. That said, a better option in those scenarios is to use a do not disturb or focus mode.
Using airplane mode does also have a secondary benefit of saving battery life, which you can do in a pinch if you're headed home without access to a charger, for example, and need to conserve what little battery life you have left. While charging, enabling airplane mode does stop your phone from continuously searching for signals. But the battery life savings aren't worth rendering your phone completely inactive. Tests have found that using airplane mode only results in a 4- to 11-minute savings in charge time. This goes for both older models and newer, more efficient phones. So, airplane mode can be a benefit when you are desperate for as much power as you can possibly get in as short a time as possible, but you'll have to weigh this against the reality that it means you can't use your phone at all, except for offline activities, while it's charging.