On-premises, also known as self-hosted, is a setup that allows databases and software to be implemented 100% on your own infrastructure. In practice, it means that you know where your data is stored, how it’s handled and who gets hold of it. This is because you keep the data on your own servers. In this way, you avoid the risk of sharing data with third parties.
With on-premises hosting you you get full control and ownership. This translates into better security and more flexibility in how you can use the data.
Finally, with the self-hosted instance you gain better efficiency, scalability and support.
More about on-premises hosting option on the Piwik PRO blog: