The Jewish prayer that is generally associated with mourning is the "Kaddish" prayer.
Ironically, this prayer's title simply means "holy," and it makes no mention of the dead. In fact, it is recited several times during every daily prayer service, regardless of whether anyone in the congregation is in mourning or is observing the anniversay of the death of a loved one.
The most important line of the Kaddish is translated:
May His great name be blessed for ever, and to all eternity.
This line is recited jointly by the entire congregation.
In general, the prayer expresses the hope that God will be glorified:
May His great name be blessed for ever, and to all eternity extolled and honoured, adored and lauded be the name of the Holy One, blessed be He.
It has become the custom for mourners to recite Kaddish at the end of each prayer service. The idea seems to be that the mourners accept God's judgement and continue to praise God despite their distress.
The earliest written mention of this custom is in a work called Or Zarua, which was written in Vienna in the 13th century--a mere "yesterday" for a prayer that is almost surely more than 2,000 years old!