Jewish Core Value
Kiddush ha-Shem literally means "sanctification of God’s name." To be sanctified means to be set apart as holy, just as good is set apart from evil and sacred is set apart from profane. God, being all good, is sanctified, and so His name, which represents Him, is sanctified.
The Jewish core value of kiddush ha-Shem refers to righteous or noble behavior that honors the name and character of God. It is also used specifically in reference to martyrdom: it is kiddush ha-Shem if a Jewish person dies because of his or her faith.
The opposite is chillul ha-Shem, desecration of God’s name through one’s behavior.
The Jewish core value of kiddush ha-Shem recognizes that the people of God are responsible to act in a manner that is worthy of God and reflects who He is to others. And that includes avoiding whatever might desecrate or bring shame to His name.
Old Testament Basis
God, who is holy, expects His people to be set apart as well, for good, which is to say, for Him.
We find this throughout the book of Leviticus:
And you shall be holy to Me, for I the Lord am holy, and have separated you from the peoples, that you should be Mine" (Leviticus 20:26; see also Leviticus 11:44-45; Leviticus 19:2, Leviticus 20:7; Leviticus 21:8).
These twin concepts linking God’s holiness/sanctity to expectations of His people is found throughout the Old Testament:
You shall not profane My holy name, but I will be hallowed among the children of Israel. I am the Lord who sanctifies you" (Leviticus 22:32). (Many more verses warn against profaning God’s name, including Leviticus 18:21; Psalm 74:7; Isaiah 48:11; Jeremiah 34:16; Ezekiel 20:9, Amos 2:7).
God’s concern for how His people uphold the holiness of His name is related to His desire for others to know Him:
But when he sees his children, the work of My hands, in his midst, they will hallow [i.e., sanctify] My name, and hallow the Holy One of Jacob, And fear the God of Israel" (Isaiah 29:23).
Ezekiel especially emphasizes that when God’s people do not live according to His will, it affects God’s "reputation" among those who are not yet part of His people:
And I will sanctify My great name, which has been profaned among the nations, which you have profaned in their midst; and the nations shall know that I am the Lord," says the Lord God, "when I am hallowed in you before their eyes" (Ezekiel 36:23).
This is one of many examples where God sanctifies His own name, that is, He acts in a way that exalts His name and character.
New Testament Teaching
The sanctity of God has not changed and His expectations of His people to reflect His holiness for all to see remains the same. The difference is, Jesus has become the model as well as the means for Jews as well as Gentiles to meet this challenge. Our behavior either points to or away from God.
Jesus said, "Let your light so shine before men, that they may see your good works and glorify your Father in heaven" (Matthew 5:16).
In the apostles we read,
For ‘the name of God is blasphemed among the Gentiles because of you,’ as it is written" (Romans 2:24).
Paul is reflecting back on verses in Ezekiel as he writes to Jewish people in order to show the need for the gospel (he has equally strong words for non-Jews in the early chapters of Romans).
…that the name of our Lord Jesus Christ may be glorified in you, and you in Him, according to the grace of our God and the Lord Jesus Christ" (2 Thessalonians 1:12).
"Yet if anyone suffers as a Christian, let him not be ashamed, but let him glorify God in this matter" (1Peter 4:16). (This is similar to the idea in Judaism that martyrdom can sanctify God’s name.)
In Traditional Jewish Life
Throughout Jewish history, the term kiddush ha-Shem has related specifically to martyrdom. Those who died in the Crusades or under duress to convert were said to die "for the sanctification of the Name." The same has been said of those who died in the Holocaust.
The medieval Jewish philosopher Rambam said that there are three ways to commit a chillul ha-Shem (to profane the name of God). First, when someone refuses to give up his or her life when one should (see above on martyrdom). Second, when one sins, not even to satisfy one’s own desires, but deliberately in open rebellion against God. And third, when someone knows the correct way to act but fails to do so, thereby leading others to question God and His reputation. 
Examples of this Core Value in Contemporary Jewish Culture
One Jewish writer defined kiddush ha-Shem as follows: "When a Jew performs an act in public requiring unusual courage, risk, honesty or integrity, as for example, when Senator Joseph Lieberman, who had indeed been a friend of the President, rose to criticize the immorality displayed by the Chief Executive, by engaging in various acts that shed no glory on the Office of the Presidency of the United States." 
In contrast, a 2010 article lamented that certain people in a Jewish neighborhood had refused to open the door to a census worker, allegedly because she was African-American. "I felt bad for the Chilul Hashem that people were making," said the Jewish author of the piece, and went on to explain that by treating everyone who comes to your door “with simple courtesy and mentchlichkeit [acting like a proper human being] you will be making a Kiddush Hashem instead of a Chilul Hashem."
When Jewish financial magnate Bernie Madoff was exposed in a grand-scale financial scam, his despicable actions were described as a chillul ha-Shem. On the other hand, when a Jewish lawyer, Ben Brafman, refused to answer reporters because he had to get ready for the upcoming Sabbath, it was called a kiddush ha-Shem. 
Conversations with Jewish Friends
Unless you are acquainted with very traditional Jewish people, most you meet will not know the terms kiddush ha-Shem and chillul ha-Shem. Still they will understand that one’s behavior can bring either honor or disgrace – to one’s community if not to the name of God. (Even the most secular Jewish people care about how good or bad behavior reflects on the Jewish community.) Some ideas for incorporating the core value into conversations with Jewish friends:
- When public figures (Jewish or non-Jewish) appear in the news for good or bad, it can be an opportunity to discuss how one’s actions sometimes affect people’s perception of others in the group they represent. From there you might talk about how God wanted the Jewish people especially to be a light to the world as a community of God’s people. You can link to what it means to you that Jesus asked His followers to be conscious of how their behavior reflects on God. This can lead to a further conversation about who God is and what He requires of us.
As you speak about human behavior, you can talk about how all of us fail at times to sanctify God’s name, because of our sin. This can lead to a discussion on atonement and the need for God’s provision for our sin.
- Some people watch their language around Christian friends out of respect for that friend – for example, catching themselves starting to say "God d___ it!" and quickly apologizing.
Should this happen with a Jewish friend, you might say something like, "It’s thoughtful of you to avoid that expression when you talk to me and I really appreciate it. I guess my sensitivity about that actually comes from a Jewish value." If your friend asks what that is, you can reply, "Well, I learned that in Judaism it’s called kiddush ha-Shem. It’s from the biblical idea that what Jews and Christians say and how we act reflects not just on ourselves, but on God, either to honor or dishonor Him. And that includes the commandment about not taking God’s name in vain." (It’s good to say that you learned something about Judaism rather than announcing that "Judaism teaches," since one shows an appreciation for your friend’s religion, while the other might be seen as showing off knowledge that he or she may or may not share.)
- You can talk about how songs or prayers from your church that speak of sanctifying God’s name (or lifting up or exalting His name) parallel similar prayers in Judaism, such as the Kaddish prayer. (Kaddish is said when someone has died, and consists almost entirely of lifting up the name of God.)
Online extras: Read the English text of the Kaddish prayer.
 Both examples in: http://rabbimichaelgreen.com/blog/2009/02/26/a-rods-chillul-hashem/