LXCFS is a simple userspace filesystem designed to work around some current limitations of the Linux kernel.
Specifically, it's providing two main things
A set of files which can be bind-mounted over their /proc originals to provide CGroup-aware values. A cgroupfs-like tree which is container aware. The code is pretty simple, written in C using libfuse and glib.
The main driver for this work was the need to run systemd based containers as a regular unprivileged user while still allowing systemd inside the container to interact with cgroups.
Now with the introduction of the cgroup namespace in the Linux kernel, that part is no longer necessary on recent kernels and focus is now on making containers feel more like a real independent system through the proc masking feature.