When logging data, it's often really really useful to have timestamps! That way you can take data one minute apart (by checking the clock) or noting at what time of day the data was logged.
The Arduino IDE does have a built-in timekeeper called millis() (CircuitPython has time) and theres' also timers built into the chip that can keep track of longer time periods like minutes or days. So why would you want to have a separate RTC chip? Well, the biggest reason is that millis()/time only keeps track of time since the board was last powered - that means that when the power is turned on, the millisecond timer is set back to 0. The board doesn't know its 'Tuesday' or 'March 8th' all it can tell is 'Its been 14,000 milliseconds since I was last turned on'.
OK so what if you wanted to set the time? You'd have to program in the date and time and you could have it count from that point on. But if it lost power, you'd have to reset the time. Much like very cheap alarm clocks: every time they lose power they blink 12:00
While this sort of basic timekeeping is OK for some projects, a data-logger will need to have consistent timekeeping that doesnt reset when the power goes out or is reprogrammed. Thus, we include a separate RTC! The RTC chip is a specialized chip that just keeps track of time. It can count leap-years and knows how many days are in a month, but it doesn't take care of Daylight Savings Time (because it changes from place to place)
This image shows a computer motherboard with a Real Time Clock called the DS1387. Theres a lithium battery in there which is why it's so big.
The RTC we'll be using is the PCF8523
As long as it has a coin cell to run it, the RTC will merrily tick along for a long time, even when the Feather loses power, or is reprogrammed.
Use any CR1220 3V lithium metal coin cell battery: