According to Google, the difference between Very Fast and Fast is that if the Quick network will stream most of the videos online, it is very fast to stream high quality videos.
Most WiFi in cafes and public places will be OK enough to browse the web, use social networks or listen to MP3s.
A private WiFi network that requires a password will not tell you the speed because you know you cannot access it and Google cannot check it randomly. Network administrators can also prevent WiFi Assistant from displaying speed by using 'Canary URL'.
See more: