What exactly does `-rdynamic` do and when exactly is it needed?

Here is a simple example project to illustrate the use of -rdynamic.

bar.c

extern void foo(void);

void bar(void)
{
    foo();
}

main.c

#include <dlfcn.h>
#include <stdio.h>
#include <stdlib.h>

void foo(void)
{
    puts("Hello world");
}

int main(void)
{
    void * dlh = dlopen("./libbar.so", RTLD_NOW);
    if (!dlh) {
        fprintf(stderr, "%s\n", dlerror());
        exit(EXIT_FAILURE); 
    }
    void (*bar)(void) = dlsym(dlh,"bar");
    if (!bar) {
        fprintf(stderr, "%s\n", dlerror());
        exit(EXIT_FAILURE); 
    }
    bar();
    return 0;
}

Makefile

.PHONY: all clean test

LDEXTRAFLAGS ?=

all: prog

bar.o: bar.c
    gcc -c -Wall -fpic -o $@ $<

libbar.so: bar.o
    gcc -shared -o $@ $<

main.o: main.c
    gcc -c -Wall -o $@ $<

prog: main.o | libbar.so
    gcc $(LDEXTRAFLAGS) -o $@ $< -L. -lbar -ldl

clean:
    rm -f *.o *.so prog

test: prog
    ./$<

Here, bar.c becomes a shared library libbar.so and main.c becomes
a program that dlopens libbar and calls bar() from that library.
bar() calls foo(), which is external in bar.c and defined in main.c.

So, without -rdynamic:

$ make test
gcc -c -Wall -o main.o main.c
gcc -c -Wall -fpic -o bar.o bar.c
gcc -shared -o libbar.so bar.o
gcc  -o prog main.o -L. -lbar -ldl
./prog
./libbar.so: undefined symbol: foo
Makefile:23: recipe for target 'test' failed

And with -rdynamic:

$ make clean
rm -f *.o *.so prog
$ make test LDEXTRAFLAGS=-rdynamic
gcc -c -Wall -o main.o main.c
gcc -c -Wall -fpic -o bar.o bar.c
gcc -shared -o libbar.so bar.o
gcc -rdynamic -o prog main.o -L. -lbar -ldl
./prog
Hello world