User space is system memory allocated to running applications. It is often contrasted with kernel space, which is memory allocated to the kernel and the operating system.
Separating user space from kernel space protects the system from errant processes that could use up memory required by the operating system (OS). The result is a more stable system where memory leaks and program crashes do not affect the OS. It is an important aspect of sandboxing, which is common in modern operating systems.
When you open an application (or "excecutable file"), the OS loads the program and required resources into the user space. Any plug-ins and required libraries are loaded into the user space as well. If you open and edit a document, that file will also be temporarily loaded into the user space. When you save the file, the data is written from the user space to a storage device such as an HDD or SSD.
NOTE: The more RAM your computer has, the more user space is available. Having extra RAM allows you to run more applications simultaneously without your computer slowing down because of a memory bottleneck.