Simply stated, textual criticism is a method used to determine what the original manuscripts of the Bible said. The original manuscripts of the Bible are either lost, hidden, or no longer in existence. What we do have is tens of thousands of copies of the original manuscripts dating from the 1st to the 15th centuries A.D. (for the New Testament) and dating from the 4th century B.C. to the 15th century A.D. (for the Old Testament). In these manuscripts, there are many minor and a few significant differences. Textual criticism is the study of these manuscripts in an attempt to determine what the original reading actually was.
There are three primary methods to textual criticism. The first is the Textus Receptus. The Textus Receptus was a manuscript of the Bible that was compiled by a man named Erasmus in the 1500s A.D. He took the limited number of manuscripts he had access to and compiled them into what eventually became known as the Textus Receptus. The Textus Receptus is the textual basis behind the King James Version and New King James Version.
A second method is known as the Majority Text. The Majority Text takes all of the manuscripts that are available today, compares the differences, and chooses the most likely correct reading based on which reading occurs the most. For example, if 748 manuscripts read "he said" and 1,429 manuscripts read "they said" the Majority Text will go with "they said" as the most likely original reading. There are no major Bible translations that are based on the Majority Text.
The third method is known as the critical or eclectic method. The eclectic method involves considering external and internal evidences for determining the most likely original text. External evidence makes us ask these questions: in how many manuscripts does the reading occur? what are the dates for these manuscripts? in what region of the world were these manuscripts found? Internal evidence prompts these questions: what could have caused these varying readings? which reading can possibly explain the origin of the other readings? The New International Version, New American Standard, New Living Translation, and most other Bible translations use the Eclectic Text.
Which method is most accurate? That is where the debate begins. When the methods are first described to someone, the person typically picks the Majority Text as the method that should be used. It is essentially the "majority rules" and the "democratic" method. However, there is a regional issue to consider here. In the first few centuries of the church, the vast majority of Christians spoke and wrote in Greek. Starting in the 4th century A.D., Latin began to become the most common language, especially in the church. Starting with the Latin Vulgate, the New Testament began to be copied in Latin instead of Greek.
However, in the eastern Christian world, Greek continued to be the dominant language of the church for over 1,000 more years. As a result, the vast majority of Greek manuscripts are from the eastern / Byzantine region. These Byzantine manuscripts are all very similar to each other. They likely all originated in the same few Greek manuscripts. While being very similar to each other, the Byzantine manuscripts have numerous differences with the manuscripts found in the western and central regions of the church. So, it essentially boils down to this: if you started with three manuscripts, one was copied 100 times, another was copied 200 times, and the third was copied 5,000 times, which group is going to have the majority rule? The third group, of course. However, the third group is no more likely to have the original reading than the first or second group. It only has more copies. The critical / eclectic method of textual criticism gives equal "weight" to the manuscripts from different regions, despite the manuscripts from the East having the overwhelming majority.
How does the critical / eclectic method work in practice? If you compare John 5:1-9 in the King James Version (Textus Receptus) and the New International Version (Critical Text), you will notice that verse 4 is missing from the NIV. In the KJV, John 5:4 reads, "For an angel went down at a certain season into the pool, and troubled the water: whosoever then first after the troubling of the water stepped in was made whole of whatsoever disease he had." Why is this verse missing from the NIV (and the other Bible translations which use the Critical Text)? The eclectic method works as follows: (1) The text of John 5:4 does not occur in most of the oldest manuscripts. (2) The text of John 5:4 occurs in all of the Byzantine manuscripts, but not many of the non-eastern manuscripts. (3) It is more likely that a scribe would add an explanation than it is that a scribe would remove an explanation. John 5:4 makes it more clear why the crippled man wanted to get into the pool. Why would a scribe remove this verse? That does not make sense. It does make sense for that the tradition of why the crippled man wanted to get into the pool would be added. As a result of these concepts, the Critical / Eclectic Text does not include John 5:4.
No matter what method of textual criticism you believe is correct, this is an issue that should be discussed with grace, respect, and kindness. Christians can and do disagree on this issue. We can debate the methods, but we should not attack the motivations and character of those with whom we disagree on this issue. We all have the same goal—to determine the most likely original wording of the Bible. Some simply have different methods to achieve that goal.