What does Mark 7:16 mean?

This verse is one of handful that are not recorded in all Bible translations. The text is "If anyone has ears to hear, let him hear!" It is found in the King James Version and New King James Version; the New American Standard Version has it in brackets. The English Standard Version and New International Version include it in a footnote.

The KJV is an English translation based on the Textus Receptus ("received text"), which was Erasmus' attempt to reconcile five or six Greek New Testaments dated from the twelfth century, and the Codex Vaticanus, which is dated to the mid-fourth century. The more modern translations combined the Codex Vaticanus with the Codex Sinaiticus (which was discovered in 1859 but printed in the late-fourth century) and remnants of the Dead Sea Scrolls. These earlier versions do not contain several verses the Textus Receptus includes, such as Mark 7:16 and Mark 16:9–20. It may be that the text "If anyone has ears to hear, let him hear!" was an editorial comment added by a scribe. Or, it might have been added during the copying process in an effort to make it more similar to later statements.

Whether the verse is included or not does not cast aspersions on the rest of the Bible. There is no impact to the theology of the Bible, especially since the exact words are found in Mark 4:9 and paraphrased in Mark 7:14. A reminder to take heed of Jesus' words certainly does not change the theme of the Bible.