If you're miserable in a survival job, internships can make you feel included and motivated.
You learn a lot of backstage type stuff that will probably give you better perspective for your own art.
Friends. Can be a great way to meet new people who share interests.
Connections. If you have a reputable organization on your resume it will open more doors.
Cons
The pay. Usually there isn't any. But sometimes you get a stipend and/or your transportation covered
The hours. Sometimes internships will be full time and you're like wait--- how am I supposed to pay bills? It just means your social life and weekends will probably be replaced with a survival job.
Getting stuck. Don't let companies use you for free after your internship is complete.