Sharing refers to the primary purpose of SHARE: a demonstrator (e.g. a researcher, a sales representative, a service provider, ...) can provide access a tool that is otherwise cumbersome to install or configure.
Hosted refers to the underlying technology: users connect remotely to virtual machines are hosted on powerful servers. Users do not need to install hypervisor tools such as VMware or VirtualBox. Instead, they need a Remote Desktop Connection client.
Autonomous refers to the built-in support for concurrent, yet isolated, use of the same research environment by multiple users.
Research refers to license considerations: researchers can SHARE licensed software in a controlled manner,
Environments refers to the holistic and simplistic nature of the approach: a SHARE virtual machine contains all the required software and documentation that is required to reproduce a research contribution.