Linux  is an operating system (OS) closely related to Unix . Or, more technically, it's the kernel at the core of an operating system; it isn't of much use by itself without the various utility programs that are typcially packaged with the kernel, many of which came from the GNU project, so some tech people regard GNU/Linux as the proper term for the operating system as a whole. (Major "religious wars" get fought over this stuff.) Linux is an Open Source OS which means that anyone can access the original source code and modify it to suit their purposes. This has resulted in the many different flavors of Linux referred to as Distributions (distros) . Linux is noted for being supported by many free software packages that replace the proprietary software used in many operating systems. There are free and open source word processors for example.
Linux started as the GNU Project  which produced many software/utility packages for a future OS they wished to develop. Linus Torvalds created the Linux kernal, the heart of the OS, in 1991. Torvalds combined his kernal with the GNU software and Linux was born.  There are purists who say that the resulting operating system should properly be referred to as GNU/Linux instead of just Linux, in order to acknowledge its heritage.
Who uses Linux?
Linux is a very small fraction (about 2%) of desktop computers worldwide, however it is a leader in cellphones and tablets, it being the core of the Android, which is the most used OS in the world overall. The Android mobile operating system and the related Apple iOS, a BSD derivative, are the two major players in these markets. Additionally, the server market, in particular Internet Service Providers, is dominated by Unix and Linux machines with about 60% of that market.
Linux as Utility
Many technicians supporting Microsoft Windows operating systems use a bootable Linux LiveCD/DVD  to access hard drives to perform repairs and retrieve data that may be lost if their repair efforts require them to format and reinstall Windows. In addition, there are distros of Linux made and used to do computer forensic work, these are used by experienced computer security people to examine and clean up computers infected with viruses or malware.
Pros and Cons of running Linux
PROS: Linux, due to its architecture, doesn't require defragging. Being a very small part of the overall market share for desktop computers, there are few Linux viruses to contend with, the virus writers concentrate on the Windows platform. Linux installs are generally much smaller than Windows installs and can run on much older hardware. Many old Windows XP machines that cannot handle Windows 7 and beyond do well with a Linux install. Linux is a free OS, there is no direct cost to the user. It is a very stable OS.
CONS: While many modern distros are user friendly out of the box, there is a significant learning curve with Linux. Many basic operations work differently and are a bit more complex on Linux. Additionally, there are some software packages, not many, that are unavailable for Linux users. There has been significant improvement in gaming for Linux of late, but many games are simply not available. There is a Windows compatibility layer for Linux, Wine,  but Windows software run in Wine doesn't always perform as well as it would in a native Windows environment (although sometimes they work better than a native Windows environment). There are also some hardware driver issues for Linux users that require advanced expertise at times to overcome. To put it in short, the main problem is you need to know what your doing.