What is the Design Condition on the epw file?

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These are design conditions read from the ASHRAE 2009 (now 2013) Handbook of Fundamentals, e.g., 99.6% and 99% heating dry-bulb temperatures, 0.4%, 1%, and 2% cooling dry-bulb and mean coincident wet-bulb temperatures, etc., when the EnergyPlus Weather Converter is used to convert the source weather file to the epw format. You can look at the ASHRAE design conditions data base in files like ASHRAE_2009_Yearly_DesignConditions.csv located in the subdirectory PreProcess\WeatherConverter. under the main EnergyPlus directory on your PC. As far as I know, what each number represents in this long string of numbers is not in the EnergyPlus documentation (although I think it should be), so if you're interested to know you have to compare them to the ASHRAE Handbook of Fundamentals Chapter 14 (2009 version) Appendix and write them down. I've never had the urge to do that, because frankly I don't even know how or whether these numbers are even used by EnergyPlus, since there's also a companion DDY file with the same ASHRAE Design Conditions expanded into IDF that can be used to do design calculations, which makes it all rather confusing, even to me.

As a final comment, these ASHRAE design conditions are not related to the weather file itself. They were derived independently by ASHRAE and are linked by the EnergyPlus WeatherConverter based on their WMO Weather Station number. I say this to warn people that regardless whether you're running an old file, e.g., TMY2, or a newer file, e.g., TMY3, the design calculations do not change.

The header of the accompanying .stat file generated by the EnergyPlus Weather Converter gives insight to what these values mean. The heating section of the header looks like so:

Design Stat ColdestMonth    DB996   DB990   DP996   HR_DP996    DB_DP996    DP990   HR_DP990    DB_DP990    
Units   {}  {∞C}    {∞C}    {∞C}    {}  {∞C}    {∞C}    {}  {∞C}    {m/s}   {∞C}    {m/s}   {∞C}    {m/s}   {deg}   
Heating 1   -4.6    -2.6    -12.6   1.3 -0.5    -9.7    1.7 1.9 9.9 10.8    8.9 8.4 2.6 310

Which matches up to the values you would expect in the heating section of the EPW file.

DB = Dry Bulb, DP = Dew Point, HR = Relative Humidity, and the subsequent numbers refer to the percentiles.

In the EnergyPlus "Auxiliary Programs" document it says the following:

fields here will be dependent on the source

This is made a little more clear looking at the actual data specification from the same document (abbreviated):

DESIGN CONDITIONS,
  N1, \field Number of Design Conditions
  A1, \field Design Condition Source
  A2, \field Design Condition Type (HEATING)
  ...
  An, \field Design Condition Type (COOLING)

So basically it goes up to n entries and you have to know based on the source what is included, what order they are in, etc.

If you have an arbitrary EPW file without documentation from its source, I don't think there is a reliable way to interpret these fields ad hoc.

I don't think older EnergyPlus documentation necessarily made this quite as clear. But I take the document I linked above to be current & therefore authoritative.