It’s often used to describe a licensing model in which a license is purchased for software that can be operated by the user on the their own hardware and/or their data center. This means that the user is responsible for the availability of the solution, must pay for all costs incurred (such as hardware, electricity, space and other operating costs), and has full control over their data and the software itself at all times.
Even though cloud services are now popular, this does not mean that on-premises software no longer has a right to exist. On-premises operation can be especially important in highly regulated industries, such as finance or public agencies, or for highly confidential or sensitive data.