Kiddush Hashem

Kiddush Hashem is any act of integrity which reflects creditably on the Jewish people and the religious faith, therefore sanctifying the Divine Name of G-d.  In times of persecution, it generally applied to situations that call for martyrdom.

The Torah says:  "You shall not profane my holy name; I will be hallowed among the people of Yisrael" (VaYikra 22:32), therefore, the concepts Kiddush Hashem and Chillul Hashem (defamation of the Divine Name).  Nothing must be done that tarnishes Judaism or the Jew. 
An example of Kiddush Hashem is told in the Midrash about Rabbi Simeon ben Shetach, president of the Sanhedrin during the early part of the first century...One day his disciples gleefully announced to him that they had found a precious stone in the collar of the donkey he had bought from an Arab.  "But I purchased a donky and not a precious stone," he said and immediately returned the gem to its owner.  Upon receiving it, the Arab exclaimed:  "Praised be the G-d of Simeon be Shetach!" (Devarim Rabbah 3:5)
Kiddush Hashem can be defined as: 
 The hallowing of the divine Name is in the familiar beginning of the Kaddish prayer and in the Kedushah, which contains the famous "holy, holy, holy is Hashem tzeva'ot" (Yeshayahu 6:3). 
The highest standards of Jewish ethics are embodied in the terms Kiddush Hashem and Chillul Hashem.

Ency. of Jewish Concepts - Birnbaum