Android has since version 6 of the Fast Pair system feature, which will make it easier and faster to pair Bluetooth headsets and speakers with the phone.
The news you are introducing now means that if you log in with your Google Account to more than one device, pairing your headset with one device makes it easier for everyone to connect with a headset. In this way, you can easily pair your headset with your cellphone and computer (support for this will come to next year's Chromebook), and if you change your cellphone, the jumped headset comes saying.
Apple has similar features for Airpods, which makes them automatically jump with both cellphones and Macs.
However, this function requires the headset or speaker manufacturer to support it. Google mentions Tarah Jaybird as a headset that supports this feature, and more is happening, among others, from Bose.