This verse is often called the "Prophetic Signature" in the Quran. It makes the bold claim that Muhammad is not a new or isolated figure, but is explicitly mentioned by name or description in the very scriptures currently held by the Jews and Christians of the 7th century.
Surah 7:157
Those who follow the Messenger, the unlettered prophet, whom they find written in what they have of the Torah and the Gospel, who enjoins upon them what is right and forbids them what is wrong and makes lawful for them the good things and prohibits for them the evil and relieves them of their burden and the shackles which were upon them...
The verse says Muhammad is written in the Torah and Gospel that the Jews and Christians currently have.
Christians have the manuscripts from that era (like Codex Sinaiticus or the Leningrad Codex tradition). If Muhammad is not in those specific books, then the Quran is making a false historical claim. If a Muslim says, "Well, the Jews and Christians changed the books to remove him," they must explain when and how this happened globally without a single trace of the "original" remaining.
If they changed the books before this verse was revealed, the verse is wrong because they couldn't "find" him. If they changed them after, then Allah failed to protect the very "clear sign" he told them to look for.
Muslims often point to the "Prophet like Moses" (Deut. 18) or the "Paraclete" (John 14) to satisfy this verse.
A Christian can easily show that Deuteronomy 18 requires the prophet to be "from among their brothers" (Israelites) and John 14-16 identifies the Paraclete as the Holy Spirit who "dwells within" the believers.
If these are the only verses Muslims can point to, and they are easily refuted by the context of the Bible, then the "Finding" promised in 7:157 is a failure. The Quran has staked its credibility on the contents of the Bible.
The verse claims Muhammad "relieves them of their burden and shackles."
This assumes the People of the Book had a legitimate, divinely-imposed burden. If their scriptures were "corrupted fables," they wouldn't have a divine burden; they would just have human errors.
By claiming to "ease" their laws, the Quran validates that the Torah and Gospel they were following were indeed the true laws of God—once again certifying the very books that contradict the Quran's core message.
Surah 7:157 is the ultimate "Paper Trail." It tells the Jews and Christians of the 7th century to look at the books in their laps to find Muhammad.
Christian for the past 1,400 years can say: we looked, and he isn't there! Since the Quran says he is there in the books "with them," and those books have been preserved in the manuscript record, the Quran has issued a challenge that history has not fulfilled.
The "Islamic Dilemma" is here at its sharpest: the Quran validates the Bible as the source of its own authentication, yet that source fails to provide the evidence required.