when filling out an online application, what does intern mean?

Answer 1

It means that you are a student looking for a temporary job (usually, for the summer) just to see if you like this line of work and make some pocket money for the next semester.

Answer 2

Intern usually applies to a non-paid (or low-paid) entry-level position taken during college to gain practical experience in your field, comparative with "apprentice".
Unless we're talking a medical intern, in which case it would be a doctor who has completed medical school and is in their first year of specialty training.