Medieval manuscripts are copies of the bible or parts of the bible that date to the medieval period (about 500AD - 1500AD). They are not the oldest manuscripts, but they were the base text used to translate the King James Bible .
The main issue is that we do not have the original copies of any biblical book (or any other ancient text for that matter). There are some small textual variations in different manuscripts, which is why there is a debate about which version of the bible to use.
The most imporant thing to keep in mind is that we do have very reliable copies, some dating back as early as just a few decades after they were probably written. Also the vast majority of the texts agree on every major point, the only variations are things like punctuation and maybe a word here or there, but nothing that changes the meaning of any portion of the bible. If you have a major translation NIV, NASB, ESV, KJV, NKJV, etc. you can rest assured that you have an accurate copy of the word of God.