Popular definitions

An internship is an opportunity to integrate career related experience into an undergraduate education by participating in planned, supervised work.
 

- Ohio State University, Department of Political Science, May 2013 (PDF)

Internships for professional careers are similar in some ways to apprenticeships for trade and vocational jobs, but the lack of standardization and oversight leaves the term open to broad interpretation.

- Internship article on English Wikipedia

Internship Japan definition

An internship is a structured program to educate and provide practical work experience for beginners in an occupation or profession. It should provide valuable experience for the intern and the company (value add) throughout the length of the internship period. Preferably, but not mandatory, an internship should build the foundation for a permanent job position. Most importantly, we strongly believe that interns should not incur any costs for entering an internship program.