Why can't a male listen to a female singer?

The singing voice of a woman is considered sensual and possibly stimulating to males. It is therefore forbidden for a man to hear a woman other than his immediate family sing and it is prohibited to pray or study Torah in that environment.

Several halachic (Jewish law) authorities are of the opinion that a recording or a radio transmitted singing voice of a woman who one does not personally know would not be actually prohibited. It is the custom however in most orthodox circles for men to refrain from hearing a woman sing in any format through any medium.

I know that in today's time this might seem severe, but the Torah puts such enormous value on the bond between a husband and wife that it does not allow for any potential damage to a man's undivided and unequivocal devotion and attraction to his one and only partner in life. Imagine how beautiful that is!

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Chana Weisberg for Chabad.org

P.S. While the above is the general rule, there are exceptions and certain leniencies. For example: The “Sridei Eish” (Rabbi Yechiel Yaakov Weinberg (1885-1966)) opines that it is permitted for women to sing along with other men. There are also those who are of the view that the restriction against men hearing women singing doesn’t apply to women who are singing in a group, since no individual is calling attention to herself.