Internships are usually conducted for people to gain experience within an industry or field that they are interested in without getting a job with the company. Sometimes, internships are paid and some are voluntary. Companies need interns because their industry may be growing bigger and bigger. There are specific job types that usually have interns. They are usually large corporations that require a long period of training. Internships allow people to start learning before acquiring a job. If you are interested in an internship and not a regular job, then you should start looking rather early in your schooling either during high school or college.
Probably during your junior year of college should you start researching and determining which places you would apply for. Then during your senior year, I would start applying for the internships.