The term hyperlocal was used by the Dark Sky app which was acquired by Apple two years ago.
I believe the term was used to mean that the weather forecast was based on your GPS position rather than the town you are in, allowing for more 'real time' forecasts like 'it is going to rain in the next 5 minutes, but this will stop in 10 minutes' (while a traditional forecast would just say '10% chance of rain at 1pm in Leeds').
The ability to get some rain and look on an app and say "it looks like this will ease off in about half an hour, so we might as well get another beer before we go to the next pub" is really useful, and on that timespan there can be different weather in different parts of town which is why a more refined forecast is required.