NetCDF allows adding metadata (such as author, date of generation, and units) to data. This allows a scientist to have a much better idea of what the data actually is given only the NetCDF file, and thus allows for easier sharing of data, building on data of others, verifying correctness of data, etc.
NetCDF also allows data to be compressed, leading to smaller file sizes, important when datasets get in the Gigabyte or Terabyte range. It also stores data (such as floating point numbers) in an agreed standard format, leading to less problems when generating data on one machine, but using this data on another.
One of the biggest advantages of using NetCDF is the large amount of (free) tools available capable of handling such data, including viewers, and data processing tools.