The real-time clock (RTC) is a way to keep the right time even if you've lost power. The low-power requirements of a clock make it easy to accurately keep time, and it can run for years on just a small battery. If your Raspberry Pi Zero is going to live somewhere it will be off and unable to access an NTP server over a network, an RTC board will help when keeping accurate time is important.
You'll need an RTC board. I used the board included in the Elego Super Complete Starter Kit, which uses the DS3231 chip. There are a few different RTC boards available, most of which will work with your Raspberry Pi Zero.
You'll also need to ensure that I2C is enabled on your RPZ. The recipe on I2C basics in Chapter 5, Getting Your Hands Dirty Using the GPIO Header can step you through getting I2C and its tools set up if you haven't already.
