FUSE (Filesystem in Userspace) is an interface for userspace programs to export a filesystem to the Linux kernel. The FUSE project consists of two components: the fuse kernel module (maintained in the regular kernel repositories) and the libfuse userspace library. libfuse provides the reference implementation for communicating with the FUSE kernel module.
A FUSE file system is typically implemented as a standalone application that links with libfuse. libfuse provides functions to mount the file system, unmount it, read requests from the kernel, and send responses back.
libfuse offers two APIs: a "high-level", synchronous API, and a "low-level" asynchronous API. In both cases, incoming requests from the kernel are passed to the main program using callbacks. When using the high-level API, the callbacks may work with file names and paths instead of inodes, and processing of a request finishes when the callback function returns. When using the low-level API, the callbacks must work with inodes and responses must be sent explicitly using a separate set of API functions.