There are a number of web applications, also called Content management systems, specific to museums.
There are a number of different styles of CMS that are effective for a museum:
1) Local database
2) Web server hostred on a private server
3) Cloud based, called Ap as Service)
Here is a discussion about such options: On Linkedin
Here are a few, more detailed reviews to follow:
Omeka – http://omeka.org/