In this instance, the internship would involve a student working toward a bachelor degree in physics which focuses on some facet of astronomy. This temporary (and unpaid) position allows the student to gain some actual real world experience in his/her field of study.
Don't give up though. In many areas, similar programs are gaining popularity at the high school level. Your best bet would be to contact a guidance counselor at your school and see if any such programs are offered in your area.
Good Luck!