The C Language
C is one of the most powerful "modern" programming language, in that it allows direct access to memory and many "low level" computer operations. C source code is compiled into stand-a-lone executable programs. C is sometimes criticized because it assumes the "programmer is always right" and allows many "questionable" programming practices.
The C Programming Language
C is a very powerful and widely used language. It is used in many scientific programming situations. It forms (or is the basis for) the core of the modern languages Java and C++. It allows you access to the bare bones of your computer.
Yet, with great power comes great responsibility. C will not coddle you (okay, raise your hand if you think Matlab was coddling... well compared to C it was very generous to you). C will require your syntax to be even more perfect than Matlab. C will make you define every variable with a Type, and not let you ever change these (in a given program). C will assume you are a master of everything you do.
Further, C is a very basic language. There are no frills, no GUIs, no Matrix processing abilities, very little file I/O support, etc. (Note: to be honest, all of these things have been written in C and are available as libraries, but the core C language is in some sense, bare boned.)