"What do we mean when we say the Bible is “inspired” by God? Do Jews have this same idea?"
I take it the we in your question means Christians, yes? If so, I venture a guess that you'll get a slightly--sometimes hugely--different answer from all the Christians you might care to ask.
Take a somewhat scientific survey, a la Gallup or Rasmussen or Harris, and ask 1000 Christians your question, and I have a feeling you'll get maybe 10 percent of your subjects who even use the words God-breathed in their answers! About one-tenth of one percent would use the Greek term theoneustos (i.e., God-breathed), though the number might be higher (or lower!).
- So-called "liberal" Christians (we're speaking very generally here, painting with a very broad brush) might say,
"'Inspired' means the Bible contains the word of God." Or
"The authors of the Bible were 'inspired' the way any writer is inspired: an idea comes to mind--whether from God or some other source or sources, and eventually the idea generates other ideas, and--if the author is really inspired--those ideas might just birth a BIG IDEA. The Bible simply contains some really good and big ideas about God and about faith." Or
"Only the words of Jesus are truly inspired. Everything else in the New Testament is a mixture of opinion and unreliable first-, second-, and third-hand testimony." Or
"The Bible is inspired in the sense that it contains really good advice on how to live. To me, it seems its biggest contribution to humankind is its teaching on love and justice." [This one came from a very bright physicist I worked with years ago.]
Do you see where I'm going with this?
- On the other hand, so-called "conservative" Christians might say things such as
- "Inspired means the Bible is literally the word of God, and every word is true, from beginning to end. God used human authors, but He gave them the words to say so that the final product is His word, not theirs." Or,
- "Inspired means that whenever I read the Bible, it's as if God is speaking to me and inspiring me. Every time I read it I can put into practice that day what I read and I can expect a wonderful blessing from God." Or
"Inspired means the Bible is reliable and that I can count on it when I'm desperate, or in need of encouragement, or when I'm about to die. It has that kind of power to lift me--or anyone--up and put us in a better place, psychologically and spiritually." Or,
"Inspired" is from the Greek word theoneustos, which means God-breathed. In other words, the Bible we have in our hands today is ultimately the product of God's breath and not man's best and highest thoughts. By "breath/breathed," of course, I'm speaking in a metaphor of sorts, because the Holy Spirit of God, like breath or wind or air, cannot be seen but His influence can be channeled through human beings in remarkable, if not miraculous ways. This is not to say the human authors were automatons who wrote down everything God "said" to them, word by word. God was pleased to use their backgrounds, their language skills, their culture, their parentage, their personalities and temperaments, as well as their strengths and weaknesses--in short everything they were, to be conduits for His word.
Moreover, while there are many, many literal words in the Scripture, there are perhaps almost as many non-literal words. We commonly call them metaphors, analogies, parables, figures of speech, tropes, and even lies which are recorded accurately! A wooden literalism is not the best way to approach God's word. On the other hand, an awareness of the importance of ancient near-east culture, biblical languages (Hebrew, Aramaic, and Greek) and the grammatical and historical facts about those languages, and the oh-so important concept of CONTEXT in which any given text is found, goes a long way toward understanding what the Bible says and arriving at an accurate and reliable exegesis.
Oh, and by the way, the only 'perfect' copies of the original manuscripts, whether written by Moses or the Apostle John, have long since disappeared and have been replaced by thousands of both old and late copies, into which minor errors have crept over the years. Not to worry, however, the vast majority (if not all) these minor errors do not affect any major doctrine of the Judeo-Christian faith as it has come down to us via the apostles and, subsequently, a succession of dedicated and highly accurate scribes who, by and large, have hewed to the major doctrines which traditionally have been believed in, taught by, and then passed down through the centuries to us today."
Guess which camp I'm proud to be a part of? You guessed correctly!
As for our Jewish brethren and sistren, I recommend, what David Stratton, above, has suggested, that you ask that question on the Jewish Stack Exchange site.