I want to say Unix (which definitely had a role in it as C and Unix evolved together) but that really is only a part of the story. Another part of the story is that Fortran was for scientific computing -- think physics, Cobol for business -- it essentially stored numbers as chars -- and BASIC for beginners.
When Microcomputers started you had two choices: BASIC and assembler. Fortran and Cobol joined them quickly but Cobol wasn't and still isn't able to generate code as well as it can reports.
Around when some AT&T people were writing C and UNIX at the Murray Hill Labs a Swiss academic named Nicholas Wirth who had been working on teaching programming came up with Pascal, which like C addressed the most current computer architecture available logically (in fact so many concepts are similar it is sometimes hard to explain that this is only because they were invented on the same sorts of machines) In the late seventies Philippe Kahn brought a commercial Pascal Compiler, Turbo Pascal, to the US and it just took over programming shops because it was so efficient. Meanwhile, Microcomputers were spreading but there was one slight problem -- most commercial software, even that which had to run on Microcomputers, was too complex to WRITE on them. People needed networks, which meant, in essence, people needed Unix to develop substantial products to run on simpler computers. GCC came out about 1983 and the prior compiler, CC, was awesome, but GCC was better and practically free. C programmers started migrating to commercial software, and especially the early ID Software games, Captain Keen, Wolfenstein 3D and Doom, proved that C could be as quick or quicker than assembly language (and Wolfenstein 3D and Doom are Open Source because they were written with GCC and use the GNU libraries -- making them derivative works). With the selling of C++ (an "improved" C for some things) and the introduction of Object-Oriented programming, there were marketing pushes and everybody was making their own compiler. The bottom line though was that C was an industrial strength method to efficiently exploit your computer's resources, as opposed to Pascal which was an industrial strength method to easily exploit them, and Fortran, BASIC and Cobol were always more limited in their focus (though when Microsoft evolved Visual Basic it lost its focus and it became important mainly for the Windows Operating System). There were other factors of course. Cobol650.zip was an awesome compiler. The last version has a note about how important it is, if this program is helpful, that you support AIDS research -- in other words its creator wasn't around after about Windows 3.1. You can model logically just about any device you can connect to a computer with C. This is really not true of any other language to the extent it is true of it. So programs written in C run better. And that is why it became more popular.
If you want to know where Java and C++ fit in -- they definitely have their places, but even today the Linux Kernel is written PRIMARILY, not exclusively admittedly, in C, so it has its place too.