The Beginning
"In the beginning God created the heaven and the earth..." Genesis 1:1
The Bible talks about the beginning of the universe, and explains that God created the heavens and earth in six days, and rested the seventh. The Bible says that God called all of creation good. On the sixth day, God created man and woman, and tasked them with caring for creation, specifically a garden called Eden.
In this garden, the man and woman (Adam and Eve) were told they had dominion and could freely eat of any tree of the garden. However there was one tree that they were told not to eat from. The tree of the knowledge of good and evil.
The Fall
"Now the serpent was more subtil than any beast of the field..." Genesis 3:1
In the garden crept a dangerous enemy. The serpent. The Bible later reveals this serpent as "the adversary", "the devil", Satan. Satan began a conversation with the woman Eve, "Yea hath God said, 'Ye shall not eat of every tree of the garden?'" the serpent asks in Genesis 3:1. The question was meant to cast doubt, and the serpent deceives the woman, and she eats the fruit of the tree of the knowledge of good and evil.
However it's not until the man Adam shared in this act, also eating the fruit, that the world became fallen, separated from God, and cursed. Adam and Eve were removed from the garden, having become spiritually dead.
The Problem
"...by one man sin entered into the world, and death by sin; so death passed upon all men, for that all have sinned:" Romans 5:12
Adam and Eve were the first to sin. They failed to follow after God's righteousness. Sin and death entered into the world, and additionally all humans thereafter were born in Adam's image. In sin. That is the unfortunate reality and sorrow of our conception, that we are born sinners, separated from God.
God must judge sinners, those who are unrighteous, because righteousness and unrighteousness can not exist together forever, at some point God will judge the world. God's judgements are true and righteous, those found in their unrighteousness will be separated from him forever.
This is the sin problem. To be spared from eternal separation and fire when we die physically, we must be found righteous in God's eyes.