Historically, most software has been issued under a closed-source license, meaning that you get the right to use the machine code, but cannot see the source code. Often the license explicitly says that you may not attempt to reverse engineer the machine code back to source code to figure out what it does!
The development of Linux closely parallels the rise of open-source software. Open source takes a source-centric view of software. The open source philosophy is that you have a right to obtain the software source code and modify it for your own use.
Linux adopted this philosophy to great success. Linus made the source programming code (the instructions a computer uses to operate) freely available, allowing others to join in and shape this fledgling operating system. It was not the first system to be developed by a volunteer group, but since it was built from scratch, early adopters could influence the project’s direction. People took the source, made changes, and shared them back with the rest of the group, greatly accelerating the pace of development, and ensuring mistakes from other operating systems were not repeated.
The source code may be written in any of hundreds of different languages. Linux happens to be written in C, a versatile and relatively easy language to learn, which shares history with the original UNIX. This decision, made long before its utility was proven, turned out to be crucial in its nearly universal adoption as the primary operating system for Internet servers.