A sin is any thought or action that falls short of God's will. God is perfect, and anything we do that falls short of His perfection is sin.
The Bible actually uses a number of examples or "word pictures" to illustrate what this means. For example, it tells us that sin is like an archer who misses the target. He draws back his bow and sends the arrow on its way but instead of hitting the bull's-eye, it veers off course and misses the mark. The arrow may only miss it a little bit or it may miss it a great deal but the result is the same: The arrow doesn't land where it is supposed to.
The same is true of sin. God's will is like the center of that target and when we sin, we fall short of His will or miss the mark. And this is something we do every day; as the Bible says, "For all have sinned and fall short of the glory of God" (Romans 3:23). Even when we aren't aware of it, we commit sin by the things we do (or fail to do), or by the way we think.
This is why we need Christ, for only He can forgive us all our sins, and only He can help us live the way we should. We can't forgive ourselves, nor can we change our hearts and make ourselves better in God's eyes. But when we know Christ, He takes away our sins and comes to live within us by His Spirit. Does He live today in your heart?