A "C-program" is not supposed to be run. It is meant to be compiled into an "executable" program which then can be run from your terminal. You need a compiler for that.
Oh, and the answer to your last question ("Why?") is that the file you are trying to execute doesn't have the executable rights set (which a compiler usually does automatically with the binary, which let's infer that you were trying to run the source code as a script, hence the hint at compiling.)
Now you need the compiler, so you need to go to App Store and install Xcode which is Apple's compiler and development tools. How can you find App Store? Do a "Spotlight Search" by typing ⌘Space and start typing App Store and hit Enter when it guesses correctly.
App Store looks like this:
Xcode looks like this on App Store:
Then you need to install the command-line tools in Terminal. How can you start Terminal? You need to do another "Spotlight Search", which means you type ⌘Space and start typing Terminal and hit Enter when it guesses Terminal.
Now install the command-line tools like this:
xcode-select --install
Then you can compile your code with by simply running gcc as in the next line without having to fire up the big, ugly software development GUI called Xcode:
gcc -Wall -o program program.c
Note: On newer versions of OS X, you would use clang instead of gcc, like this:
clang program.c -o program
Then you can run it with:
./program
Hello, World!
If your program is C++, you'll probably want to use one of these commands:
clang++ -o program program.cpp
g++ -std=c++11 -o program program.cpp
g++-7 -std=c++11 -o program program.cpp
For compiling a C program on your latest macOS, just type the following in the terminal after saving the file with a .c extension and on reaching the path where the file is saved:
cc yourfilename.c
Once you have checked all the errors after compilation (if any), type the following for executing the code:
./a.out
These commands are tested on macOS v10.14 (Mojave) and are working perfectly fine.