The NIV editors themselves make no such claim. In the first few pages of the Bible you’ll find - as in most Bibles these days - a brief overview of the translation process, the methodologies used, the manuscripts that were used, etc. I won’t quote the entire thing here, but they make it clear they were selecting from the same bunch of manuscripts everyone else has. A representative quote would be “The New International Version is a completely new translation of the Holy Bible made by over a hundred scholars working directly from the best available Hebrew, Aramaic, and Greek texts.”
Consequently, they did - at times - a pretty bad job.
they mean the same thing that everyone else means by “original”. the closest in proximity to the time it was written and (where available) pieces of manuscripts thought to be from the exact time of the original.
the reason the NIV is not a great translation (although not a bad one) is because they translated “phrase by phrase”. they attempted to put the meaning (in the translators’ view, and there were many of them, all experienced and scholars in the original languages) of the phrases as opposed to translating word for word and just putting the meaning of the words in and allowing the words to form the meaning of the phrases. many protestants (who understand the differences in the methods) have either switched to the NASB (new american standard bible) or the ESV (english standard version) as they are both word for word translations. in fact, some of the contributors to the NIV moved on to help with the NASB and the ESV because they saw how a phrase by phrase translation was lacking in many ways.