GNU ("GNU is Not Unix", a recursive acronym) is a large software project started by Richard Stallman, the inventor of free (as in freedom) software, running since 1983 with the goal of creating, maintaining and improving a completely free (as in freedom) operating system, along with other free software that computer users might need. The project doesn't tolerate any proprietary software (though it sadly tolerates proprietary data). GNU achieved its goal of creating their free operating system when a kernel named Linux became part of it in the 90s as the last piece of the puzzle -- the system should be called just GNU but is now rather known as GNU/Linux (watch out: most so called "Linux systems" nowadays aren't embraced by GNU as they diverge from GNU's strict policies on what the system should look like, only a handful of operating systems are recommended by GNU). However, the GNU project didn't end and continues to further develop the operating system, or rather a myriad of user software that runs under the operating system -- GNU develops a few of its projects itself and also offers hosting and support (such as free legal defense) for GNU projects developed by volunteers who dedicate their work to them. GNU gave rise to the Free Software Foundation and is one of the most important software projects in history of computing.
The mascot of GNU is literally gnu (wildebeest), it is available under a copyleft license. WARNING: ironically GNU is extremely protective of their brand's "intellectual property" and will rape you if you use the name GNU without permission (see the case of GNU boot). It's quite funny and undermines the whole project a bit.
The GNU/Linux operating system has several variants in a form of a few GNU approved "Linux" ditributions such as Guix, Trisquel or Parabola. Most other "Linux" distros don't meet the strict standards of GNU such as not including any proprietary software. In fact the approved distros can't even use the standard version of Linux because that contains proprietary blobs, a modified variant called Linux-libre has to be used.
GNU greatly prefers GPL licenses, i.e. it strives for copyleft and largely recommends it, even though it will also accept projects under permissive licenses as those are still free. GNU also helps with enforcing these licenses legally and advises developers to transfer their copyright to GNU so that they can "defend" the software for them.
If we still have a bit of freedom in computing nowadays, it is largely to GNU -- this can't be stressed enough. But although GNU is great and has been one of the best things to happen in software ever, it also has many flaws, for example:
The project officially started on September 27, 1983 by Richard Stallman's announcement titled Free Unix!. In it he expresses the intent to create a free as in freedom clone of the operating system Unix, and calls for people to join his effort (he also uses the term free software here). Unix was a good, successful de-facto standard operating system, but it was proprietary, owned by AT&T, and as such restricted by licensing terms. GNU was to be a similar system, compatible with the original Unix, but free as in freedom, i.e. freely available and allowing anyone to use it, improve it and share it.
In 1985 Richard Stallman wrote the GNU Manifesto, similar to the original project announcement, which further promoted the project and asked people for help in development. At this point the GNU team already had a lot of software for the new system: a text editor Emacs, a debugger, a number of utility programs and a nearly finished shell and C compiler (gcc).
At this point each program of the project still had its own custom license that legally made the software free as in freedom. The differences in details of these licenses however caused issues such as legal incompatibilities. This was addressed in 1989 by Richard Stallman's creation of a universal free software license: GNU General Public License (GPL) version 1. This license can be used for any free software project and makes these projects legally compatible, while also utilizing so called copyleft: a requirement for derived works to keep the same license, i.e. a legal mechanism for preventing people from making copies of a free project non-free. Since then GPL has become the primary license of the GNU project as well as of other unrelated projects.
GNU has developed an almost unbelievable amount of software, it has software for all basic and some advanced needs. As of writing this there are 373 software packages in the official GNU repository (at https://directory.fsf.org/wiki/Main_Page). Below are just a few notable projects under the GNU umbrella.
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