The Hebrew and Greek words translated "sin" throughout the Bible focus largely on two concepts. The first is transgression.
To transgress means "to step across" or "to go beyond a set boundary or limit." This concept can be compared to an athletic playing field with lines delineating the boundaries within which the game is played. When a player crosses over those boundary lines, he has committed a "transgression" and gone out of bounds. Limits are set that define the playing area, and the players are to stay within the limits of that area.
Most of the other words translated "sin" in the Bible involve a second concept, "to miss the mark." Again, to use a sports analogy, if a player aims for the goal and misses, how many points does he get? None. He missed the goal; he missed the mark he was aiming at.
This view of sin includes the concept of our going in one direction but straying off course and not continuing in the intended direction, with the result that we don't make it to the goal. We miss.
This concept also encompasses the idea of failing to measure up to a standard. For example, most academic courses and tests are graded according to a minimum standard. If we don't meet that standard, we fail that test or course. By not meeting that standard we "miss the mark" and don't pass.
Both of these concepts, transgressing and missing the mark, involve basic requirements. If we transgress, if we cross set boundaries or limits, then we must have boundaries or limits to cross over. If we miss the mark we must have a mark, target or standard to miss. Sin, then, is to transgress the boundaries God has set for us, to miss the target He has established.
This is where the biblical definitions of sin become important—because these scriptures define the boundaries and standards God sets for us. They define the playing field on which we are to live. They also define the goals we are to aim for, the minimum standards we are expected to meet. In other words, the biblical definitions of sin show us the standards God has given us that define what is acceptable to Him and what isn't acceptable. They show us what measures up and what falls short of those standards, the fundamental principles God has given us to live by.
The definitions of sin in the Bible are not simply arbitrary dos and don'ts. Instead, they show us the way God wants us to live, the spiritual principles that reflect His character.