MEX files are like an interface between matlab and code written in C/C++ or FORTRAN. You can use the 'mex' command to compile source code from these languages into a mex file. After that, the mex file acts like any other matlab function and can be invoked from the command line or any script.
I recommend going through the Matlab documentation, especially try out the examples you may find there. You may start from here:
MATLAB Coder is used to generate C/C++ source code from any matlab script. You may invoke the 'codegen' command on any matlab script to start off. Once again, you may read the documentation or try this for a starting point: