on-premises software

On-premises software is installed and run on computers on the premises (in the building) of the person or organisation using the software, rather than at a remote facility, such as at a server farm somewhere on the internet.
Premises的意思是生产场所, 营业场所. Premises不是Premise的复数形式, 是有独立含义的单词. 根据

Wikipedia的解释, On-premises Software指的是运行在用户或组织所在的经营场所计算机中的软件.

与On-premises Software相对的便是SaaS或PaaS，将软件抽象为服务

provision

以下内容引自http://blog.csdn.net/catharryy/article/details/48661557

Provisioning is a term most often used in the telecommunication field. In this capacity, it refers to the configuration of both hardware and software in order to activate telecommunication service for a customer. Provisioning is not equipment. Rather, it consists of commands and controls for specific telecommunication devices.
　　The configuration process of provisioning allows the user to access data and technology remotely. The user also has the ability to look up secured data and to grant authorization to a wide range of network applications and databases by utilizing a unique identity process. Provisioning is generally managed and incorporated into departments such as information Technology (IT) and human resources. It gives network administrators the ability to assign technology privileges to employees and contractors of companies, as well to business partners. The software can also be used by a company’s IT department in order to enforce maximum security of system resources.
　　Provisioning also assists in monitoring the protection process of access privileges. This security feature is widely used along with hardware resources in products such as computers, pagers, and mobile phones in order to increase security and privacy. With its unique boot image control, provisioning reduces the number of configurations utilized during the transfer of information and, as a result, decreases the amount of abuse to the system.

简单来说，就是维护和预置,或者称之为设置的过程。