Because, as you said yourself, it is not feasible to put the "whole software" into one source file.
If your program is very small, then yes it's is simpler just to put everything in one .c file. As your program gets larger, it becomes helpful to organize things by putting related functions together in different .c files. Further, in the .h files you can restrict the declarations you give to declarations of things that are supposed to be used by things in other .c files. If a .c file doesn't contain anything that should be accessible outside itself, it needs no header.
For example, if .c has function foo() and fooHelper(), but nobody except foo() is supposed to call fooHelper() directly, then by putting foo() and fooHelper() into foo.c, only putting the declaration of foo() in foo.h, and declaring fooHelper() as static, it helps to enforce that other parts of your program should only access foo() and should not know or care about fooHelper(). Kind of a non object-oriented form of encapsulation.
Finally, make engines are generally smart enough to rebuild only those files which have changed since the last build, so splitting into multiple .c files (using .h files to share what needs to be shared) helps speed up builds.