The C language didn't just happen over night. Time, people, and events where needed in order for this language to become a reality. So, how exactly did C come to its existence? In the early 1960's the idea of time-sharing become powerful. Large amounts of money and manpower were spent on programs that allowed a large number of people to access one computer from a terminal and use some of its resource, all at the same time! One computer was able to act like 100, allowing places like Universities to efficiently give its students access to a computer at a reasonable cost. Eventually, a time-sharing operating system called Multics became prominent in the time-sharing industry. Although Multics was revolutionary in some was, it had many problems. It code was large and complex, which meant it wasn't very efficient to modify the operating system. In the early 1970's, the people at Bell Labs got frustrated and fed up with Multics, so they decided to create their own operating system. Today, this operating system is known as Unix. It was originally written in assembly, which led to some problems, since it isn't very portable. The solution to their problem was going to be a programming language called B, but it had some problems and inefficiencies. Dennis Ritchie created a newer and better version of B that was called C; C being a lot more powerful than B. C was so powerful, that it was able to do the job and Unix was mostly rewritten in C. This allowed Unix to be ported to many different computers with relative easy. Soon C was used for other jobs, slowly becoming one of the most influential languages ever.
C is widely used in education, in application programs like text editors, windows based applications, in games like Quake III, in calculations like finding interest, and for sorting, maintaining and organizing large amounts of data. C programs are used in engineering applications like plotting of curves, integration and many more things. C has been used in very complex things also, e.g. Operating systems like Microsoft Windows, GNU/Linux and other Unices (SunOS, FreeBSD, et al) have also been written partly in C.
A C compiler is a program that takes source code and turns into an executable file. To learn C, you'll need a computer and operating system that has a C compiler, although it's recommended that you have an operating system like Windows, Linux, or Apple. All though it's not recommended, you could use an operating system like MS-DOS and UNIX as long as there's a C compiler.