The key to understanding suffering is to first understand where it came from. Why does suffering exist in a world built by a supreme God? If I'm suffering, does that mean I've done something wrong? What about when innocents suffer? All of this goes back to what is commonly known as "The Fall".
Initially, all that God had made was "very good". There was no suffering, and there was actually no death. There were only two people, Adam and Eve, and these were given dominion over the earth and everything in it. They were to work in a garden, where they had an easy life. The trees produced fruit, and as they were completely naked, they were obviously in a rather nice climate.
However, God gave them a "thou shalt not" command. Adam and Eve were permitted to eat from all the trees in the garden except one: The Tree of Knowledge of Good and Evil. They were told that if they ate of it, they would die. Of course, under temptation of Satan, they did eat, and God followed through with His promise. The entire creation was cursed, and so now, nothing works perfectly.
One thing to note is that although it does not work perfectly, it does still work. Before the fall, the garden still required maintenance. It was only after the fall that became a painful endeavour. Before the fall, Adam and Eve could still be fruitful and multiply. It was only after the fall it became painful. Animals weren't cursed before the fall either. No carnivory, no violence, these things were alien to our world until Adam fell. And so the simplest explanation for why suffering exists is because of sin.
But of course, God didn't just abandon us like a broken pot. Earth 2.0 is in the works, and because of the last Adam, who was sinless, our ticket there has been stamped. The fall will be completely reversed, and God's Kingdom will be greater than Eden ever was. Sin will not only be removed, but will be impossible, and thus suffering will not even be a bitter memory.