What is the meaning of -999 degrees Celsius?
The value -999 is likely the "fill value" used in the dataset when data is missing or is not being properly filtered or handled when displayed.  In the specific case on the website you cite, it is likely a problem with the algorithm for wind chill (the "feels like" temperature this time of year). 

It isn't a physical value and only means the value is missing. Furthermore, -999°C is not a possible value because absolute zero is –273.15°C, and it's not possible to be colder than this (at least not in any meaningful way, and certainly not because of wind chill). The coldest recorded temperature on earth is around –90°C.