Traditionally, the seven weeks in between Passover and Shavuot are a somber time for Jews, as 24,000 students of Rabbi Akiva were killed. Along other prohibitions, musical instruments are not to be played or listened to. This is where Jewish a cappella music fits in. The human voice is not considered an instrument for the purposes of these 49 days. As opposed to other activities, however (such as watching paint dry), Jewish a cappella music can be a deeply meaningful experience.
The same reasoning can be applied to why Jewish a cappella music is a good choice for holidays such as Shabbat and the Days of Awe (Selichot, Rosh Hashana, & Yom Kippur); it allows for a rich experience without violating the "no-instruments" prohibition.