In rabbinic sources and modern parlance, it refers to private and communal conduct that reflects well, instead of poorly, on the Jewish people.
The phrase "sanctification of the Name" does not occur in the Hebrew Bible,[1] but the instruction "to sanctify [God]" and the converse command "you shall not profane My holy name"[2] is frequently expressed.
Any action by a Jew that brings honor, respect, and glory to God is considered to be sanctification of His name.
In contrast, any behavior or action that disgraces, harms or shames God's name and His Torah is regarded as a chillul Hashem (desecration of the Name).
Martyrdom during the Hadrianic persecution is called sanctification of the Name in Bavli Berachot 20a and Midrash Tehillim.