OpenERP can be easily installed on your own server, or even on a PC, as well as on the cloud.
If you feel that your data is quite sensitive and would rather keep it close to your chest then hosting OpenERP on your local server is the preferred option. Note that by deploying OpenERP on your own server, then you need to make sure all backups are done, have the technical know how to make sure the system is maintained regularly, and in case of a breakdown you have the expertise to bring it up with minimal loss of productivity.
There are many reasons why you would use local hosting environment for OpenERP:
Having said that, it might be worth noting that cloud hosting operators guarantee the privacy and security of your data, and in many cases they have the capacity to protect it better than you do. However, for other reasons, we understand that local hosting is the way to go. We are happy to support you either way and will work with you whatever your choice may be.