:mak[e][!] [arguments] will start the program referred to by the makeprg option. By default, makeprg is set to "make," but can be configured to invoke any appropriate program.

All [arguments] (can be several) are passed to makeprg just as if it had been invoked with :!{makeprg} [arguments].

The output of the invoked program is parsed for errors according to the 'errorformat' option. If any errors are found, the quickfix window is opened to display them.

:cnext :cprev can be used to cycle between errors displayed in the quickfix window. :cc will jump to the error under the cursor.

It should be noted that on systems where gnumake is installed and properly configured, there is generally no need to define &makeprg to anything but its default value to compile mono-file projects. Thus, in C, C++, Fortran... just type :make %< to compile the current file. According the source file is in the current directory, :!./%< will execute it. Compilation options can be controlled through $CFLAGS, $CXXFLAGS, $LDFLAGS, etc. Consult the documentation of make regarding implicit rules.