Sometimes you need access to filesystems that are not natively supported by your operating system. For example when you need to access an weirdly formatted external drive.
To integrate support for a new filesystem, you normally need special binary drivers that are loaded into your kernel. This usually involves a reboot and some security issues, as the filesystem driver runs with the same privileges as the kernel itself.
But wait. FUSE is a convenient alternative to kernel-based filesystem drivers. FUSE stands for "Filesystem in Userspace" and makes installing, using, and developing filesystems really easy.