Private WiFi Addressing is considered a valid security technique with benefits for most users.
*Note: The following is massively simplified for illustrative purposes only *
Most people are familiar (at least in concept) with IP addresses, which are key to how traffic gets routed on the internet.
At a lower level, though, each device has its own physical address (known as a MAC address) that is unique to each device.
While your IP address may change as you change locations (home, roaming, work, coffee shop, etc.), your physical MAC address would ordinarily remain the same. Theoretically, some nefarious user could track this MAC address and narrow down your location. Someone on your office network might log your MAC address (it's visible to anyone on the local network), and then see it connected later at a local coffee shop and they'd know you were nearby. Or maybe they see your phone connect to the airport WiFi and they surmise you're headed out of town.
Private WiFi Addressing changes this, such that the device uses a pseudo-random, private MAC address on each different network. This makes it harder to track where your device is/has been - the MAC address used at the office would be different from that used at the airport, so that tracking method is shut down.
The downsides are generally low for most users. It's mostly transparent, unless you're in an environment where the MAC address is used to grant access to the network (some corporate networks, for example, may allow only known devices to connect, based on the known MAC address, so this method would break that security).