Application delivery is increasingly provided by “cloud” services that eliminate the need for on-site IT infrastructure. Savings are achieved because of reduced maintenance and support costs, whilst productivity is improved through global accessibility and decreased downtime.
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.