Decent ERP systems provide multiple options for software services and databases.
SAAS - software as a service (SaaS)
Software as a service (SaaS) is a software licensing and delivery model in which software is licensed on a subscription basis and is centrally hosted. SaaS is also knows as on-demand software, web-based software, or web-hosted software.
On-site / on-premise
It offers the facility to create and maintain ERP on client servers. These servers may be physical or virtual, but it's the responsibility of the client to provide all the infrastructure for getting ERP online. This includes configuration of DNS, availability and backup of electricity, internet connectivity and bandwidth. The health and performance of the servers have to be taken care of.
Cloud hosting
An other hosting option for ERP is cloud hosting. Client can chose from many hosting provider according to the needs and budget. This option reduces the efforts of maintaining the servers.