What is apprenticeship on job application?

usually only applies to union jobs nowadays.this is where you agree to be trained in a skill for so long a period of time. usually 3 years. in old days, if you wanted to be a blacksmith, then you signed on to be the blacksmith's apprentice for whatever period of time. you did whatever work the blacksmith wanted until you learned to be as good as him. then when he agreed, you were released and could start your own blacksmith shop, and take on your own apprentice.
An aprenticeship is a period of learning the skills and knowledge required to Cary out a particular business. They tend to aply more to trades then profesions. In the past people were known to pay tradesman for the privelege of working under them as an aprentice.