Peaceful describes something calm and tranquil, not at war. The ocean seems peaceful when the waves lap gently at your feet, and a country can be peaceful when it's not fighting anyone.
Peace comes from the Latin word pax meaning, "tranquility, absence of war." Add the suffix ful which means — you guessed it — "full" and you have something full of peace, like a protest where nobody gets hurt. It refers to being passive, committed to nonviolence, like Martin Luther King Jr.'s peaceful protests during the Civil Rights Movement. It's also the mellowness that inspired the Eagles to sing, "I got a peaceful, easy feeling that you won't let me down."