What is the real Jewish meaning of Jeremiah 8:8? Does it claim the Bible is corrupted?
The context of that passage does not refer to Biblical corruption. The general chapter in Jeremiah concerns God's expressed frustration at the people for not listening to Jeremiah's prophesies. It is in this context that the scriptural passage appears, which is:
אֵיכָה תֹאמְרוּ חֲכָמִים אֲנַחְנוּ וְתוֹרַת יְהֹוָה אִתָּנוּ אָכֵן הִנֵּה לַשֶּׁקֶר עָשָׂה עֵט שֶׁקֶר סֹפְרִים
How can you say, "We are wise, and we possess the Instruction of the Lord"? Assuredly, for naught has the pen labored, for naught the scribes! [NJPS translation]
Obviously, the passage shouldn't be read on its own, and reading chapters 7 and 8 clarifies the subject as rebuking the people's stubbornness for not listening to the word of God. There are many Jewish commentators on this chapter, but here is one example, from the Radak:
אם תורת ה' אתכם מה תועיל אם לא תקיימו אותה מי שעשה הקולמוס לכתוב אותה לחנם עשה אותו וכן שקר סופרים הסופרים כתבו אותה לחנם כי אחרי שאין אתם מקיימין אותה הרי היא כאילו אינה כתובה לשקר לחנם כמו אך לשקר שמרתי
If the Law of the Lord is with you what good is it if you do not fulfill it [the laws]? The same person who made the quill to write it did it in vain. And that is the meaning of the false scribes: the scribes wrote it for naught because afterward you didn't fulfill it. So it is as if it wasn't written but to lie in vain, as if to lie [and not the Law] is what I possess.
In summary, this has nothing to with a corrupt Bible but with a corrupt people who do not follow the Bible.