The Jewish religious ritual consists of various holidays and objects that are used throughout the year and the day. Jews snuck in teffilin (a Jewish parchment wore by men during the morning prayer). Some even brought prayer books and torahs. Jewish ritual depends on the ability to keep time and it was very difficult during the later part of the war for the prisoners to keep up with the Jewish calendar (lunar calendar), but nonetheless they would make their own calculations, and there are stories of Jews who fasted during Yom Kipur, even with the terrible malnutrition they faced.

It's important to remember that many of the Jews who ended up in the camps, especially from Eastern Europe, have been devout religious individuals their entire life, belonging to various sects, and whose sole purpose in life was religious observance. Many would risk their life to practice their rituals under danger of death.

There was also fear that Jewish culture as a whole was headed towards obliteration, so many prisoners saw retaining their religious practices as a crucial step in preserving as much of their culture as they could. While the holocaust presented an entirely new scale of oppression, Jews in Europe were no strangers to religious persecution, and thus there were already methods for preserving religion where it was not allowed.

A survivor at my synagogue recalled some of the older men skimming grease and fat off of the broth they were fed and making Shabbat candles from it. Keep in mind these people would have often committed many passages of the Hebrew Bible to memory and all would know the prayers used on a daily basis or during services. It was all they had left, so they held on to it.