The CMOS battery, or RTC battery, provides power for the real-time clock so that your computer can continue to keep time when it is unplugged.
The name "CMOS battery" is a misnomer on modern computers. Older computers used the battery to maintain BIOS settings, which were stored in a CMOS SRAM chip that would lose its contents if disconnected from power. This setup does have the advantage of making it easy to clear the BIOS settings, either by removing the battery or by inserting or removing a jumper. Newer systems store firmware (BIOS or UEFI) settings in flash memory or EEPROM, which does not require power to maintain data. See: Wikipedia article on nonvolatile BIOS memory and How can a CMOS battery store data?
This battery was, and still is, used to maintain the real-time clock. As this is the sole purpose of the battery today, it is sometimes called the RTC battery. This ensures that your computer can continue to keep time even when unplugged. The battery is usually a readily-available CR2032 button cell, and is typically usable for 2 to 10 years. If your computer loses track of time when unplugged for more than a few hours, it is time to replace the battery. See: How long does CMOS battery (3V) on a motherboard last?
CMOS battery on Pico ITX motherboard – Image source