We use Merge for an app I built so I can elaborate.
Using your example, let's say I want to get the weather for Berlin today from NOAA, Foreca, and DarSky. I would have to do:
noaa.com/api?city=berlin
foreca.com/api?city=berlin
darksky.com/api?city=berlin
return each results and store them.
As opposed to sending the call once:
getweather.com/api?city=berlin
Now let's say I want to add a new source (Wunderground). I login to Merge/Nango and just check "Wunderground" and just change my API call to store the new source.
Now let's say Foreca changes it's API to foreca.com/v2/api?city=berlin I don't have to monitor this at all. Merge/Nango would do this for me.