If it's primarily an art gallery, you may do or oversee the following tasks (depends on size/resources of gallery)
1) install art
2) organize "openings" (receptions for new shows)
3) coordinate mailings
4) help prepare artist bios
5) pack/arrange for shipping of art
6) arrange insurance for artwork
7) review slides
answer phones, sweep up!
If it's an art organization, many have outreach/education as part of their mission, often a crucial aspect of their funding.
1) fund development (be specific)
2) community outreach
3) coordinate youth classes
4) purchase materials
5) publicity

Most organizations appreciate if you have computer skills and particularly if you can help create or maintain a website.

Good luck!