Wi-Fi MESH networks are akin to having a cell network across your house for Wi-Fi. It is not the same as using Wi-Fi extenders — more a case of having multiple satellite Wi-Fi access points that flood your house with Wi-Fi signals. It has been around for at least 4-years, with Google one of the pioneers.
I have looked at it and to intend to upgrade to such a MESH network one of these days.
EERO, by no means, is the only provider. Most Wi-Fi providers now offer some level of MESH networking.
Pretty obvious why Amazon wants the technology. They will incorporate it with Alexa. You will then have Alexa all around your house — without any blind spots! You could interact with Alexa from the bathroom. Scary. Plus, Google has it.
I am surprised that Amazon did not go with Ubiquiti Networks. That would have been my choice. Maybe Ubiquiti was overkill, whereas EERO has just enough for what Amazon wants to do with Alexa.