How does printf() actually work?

When I execute the c file

#include 
#include 

int main(){
        printf("before the system call. I am too excited!\n");
        system("ps");
        printf("after the system call. Look what you have done!\n");
}

I get the output

before the system call. I am too excited!
    PID TTY          TIME CMD
    140 pts/0    00:00:03 zsh
   1613 pts/0    00:00:00 system
   1614 pts/0    00:00:00 sh
   1615 pts/0    00:00:00 ps
after the system call. Look what you have done!

but when I remove the '\n' from the first printf(), I get

PID TTY          TIME CMD
    140 pts/0    00:00:03 zsh
   1590 pts/0    00:00:00 system
   1591 pts/0    00:00:00 sh
   1592 pts/0    00:00:00 ps
before the system call. I am too excited!after the system call. Look what you have done!

So what I am asking is, how the '\n' character changes the printf() output, and it led me to thinking, does the program stores the text in some buffer before printing, or just prints with the go? I am getting the expected output for the second if I add fflush(stdout) for before the system("ps"), but I want to understand the exact mechanism. When I add fflush(stdout), it cleared the buffer of the first printf() and the output of system("ps") was appended with it, but without it, what is exactly happening?