Linux in its pure form is a monolithic kernel made by Linus Torvalds. It is the hypothalamus of any GNU/Linux distribution- allocating resources to processes. (the stuff you see with ps -x) Linux distros are useless without a Linux kernel and Linux kernel is useless without a userland, mostly provided by GNU. And then there's distros...
In Common Parlance
You'll probably here that some distros are closer to "pure linux". Linux is a Unix-like Operating System, emphasis on "like". UNIX is a brand of sorts- a club of systems meeting certain specifications based on a computer from the 70s. There is nothing inherently better about UNIX. (The *NIX family on the other hand is objectively better.) Sure Solaris is delightful for its old-school charm alone, but so is DOS. (Think IBM and early Microsoft) Indeed the most popular UNIX operating system does not represent the noble values of GNU / Linux. That would be... Mac OSX! (cue booing) BSD is awesome though. Anyway, Linux belongs to a related but less exclusive club of POSIX compliant Operating Systems. That's a way Linux can be pure- adherence to the POSIX standard. The majority of distros are indeed POSIX compliant. Another way "pure" is used is "light-weight". Less bloat. A distro with a smaller userland is closer to pure linux kernel, is it not? Another way pure is used is "doing things in a super antiquated way for nostalgia value". In a word, Slackware, the UNIXiest of them all. Its package manager can't resolve dependencies, like in the good old days. Begone, haters!