Some of the definitions are:

Digitizing or Punching : is the process of  Converting artwork into data containing commands that tell an embroidery machine frame how to move through the 
machine operating system. The word Punching actually comes from the traditional 
jacquard embroidery machines. The code that tell the machine frame how to move
comes from a tape that were punched with holes. These holes were the code or instructions. 

Digitizing or punching design is the process of converting artwork such as vector format artwork or scanned artwork (.bmp, tif,) into  digital embroidery. This can  
be done by the use of embroidery digitizing software and a skillful digitizing artist 
to interpret that particular design.