Standalone application creation in MATLAB involves writing your MATLAB code as a function, then using the MATLAB Compiler tool to convert that code into a standalone executable file. This executable can run on computers without MATLAB installed. The process starts by writing the function, then running the compiler command 'mcc -m yourfile.m' which packages your code and MATLAB runtime into an executable. When you run this executable, it behaves like a normal program, showing output and then closing. This method allows sharing MATLAB programs easily without requiring the MATLAB environment.