I've seen it mentioned that some translations use the Textus Receptus and others don't, so why is this document important?
The Textus Receptus, the 'Received Text' is the Greek text of scripture that is represented in several published editions, principally Erasmus 1514 and following editions up to 1527, Stephens ('Stephanus') 1550, Beza 1598, Elzevir 1624 and Scrivener 1894. See Textus Receptus Bibles.
The Authorised Version can be considered to be an edition of the Received Text in English for the translators did not publish their Greek text in 1611. Scrivener published what he understood to be their source material in 1894.
The oldest known edition of the Received Text - in English - that I know of is the Wessex Gospels produced in about 990 AD in Middle English, which edition, notably, contains both the long ending of Mark 16 and also the account of Jesus and the woman taken in adultery in John 7:53 - 8:11 the so-called Pericope de Adultera. It is translated from the Greek and consists only of the four gospel accounts.
There is a division of thought regarding the ancient, original Greek scriptures. Up until 1881, the King James Authorised Version was 'the bible' as far as the vast majority of English speaking people were concerned.
Then, it was decided to improve the translation and certain chosen people were gathered to carry out that necessary task, for there were corrections and improvements necessary. However, two of the appointed persons privately approached every other member of the committee and introduced the individual participators to their own, new Greek text. Westcott and Hort are their names.
The outcome of this was that the Revised Version of the bible was not an improvement of the Authorised Version but was a translation of a new Greek text. The text of the AV is close to what is called the Received Text or the Textus Receptus. The Greek original manuscripts - there are thousands of them - on which this text is based, are from the 4th, 5th, 6th centuries and following centuries.
Westcott and Hort argue that a few manuscripts which are older than that are of massive importance and they argue that those few manuscripts should be allowed to predominate over the huge majority of later writings. They made particular reference to a manuscript discovered by Tischendorf in about 1860 and to one in the Vatican which became available to scholars at about the same time. These are the Codex Sinaiticus and the Codex Vaticanus.
The opposite argument is that these ancient copies - from the 2nd century or so - are deeply flawed and that is why they survived. They were little used because they were not highly regarded. The good copies were read and re-read and used so much that they deteriorated and had to be replaced.
This side of the divide also queries whether Divine Providence would permit thousands of manuscripts, and quotations of scripture in other books, to be available for many centuries, yet suffer the 'most important' evidence to be unavailable to the Christian Church until the 19th century.
The differences in the subsequent Westcott and Hort text, caused by alterations, omissions and additions to the Received Text amount to 7% of the text as can be seen in Scrivener's comparative text of 1894 in which he highlights the differences.
All of the above can be read in various Wikipedia articles but this is a controversial subject and opinions are being propagated within what ought to be unbiased expressions of truth. I have tried my best not to take one side or the other in what I have expressed here. But I have personally followed one side of this divide for the past fifty years, ever since I was a teenager.
Wikipedia, and other sources, will refer to 'uncials' which are ancient manuscripts written in capital letters and 'miniscules', which are manuscripts written in smaller writing which is 'cursive', that is, ordinary handwriting; they will refer to 'versions' which are the translation of the Greek scriptures into other languages, such as Syriac; they will refer to 'Patristic Citations' which are the quotations of the fathers of the Christian Church (such as Augustine, Jerome, Eusebius) in the books which they wrote; and they will refer to 'Lectionary Quotations' which are bible texts preserved in ancient books of church service, similar to the Common Prayer Book of more modern times.
Then there is the 'Septuagint' the Greek translation of the Hebrew scripture, which may, or may not, have been quoted by apostolic writers; and there is the 'Vulgate' which is the Latin translation of the Greek scripture, written, largely by Jerome, in the 4th century.
All of this evidence is used in collation, such that errors in copying can be eliminated by comparisons made across the whole spectrum of evidence until agreement is reached as to what were the original 'autographs' - the actual written words of the apostolic writers who wrote in the first century after the resurrection and ascension of the Lord Jesus Christ.