Our friends were injured in an accident. They will be okay, but there is a long road to healing. So we ask that their names be put on a “Mi Sheberakh list” for the time being.
The term “Mi Sheberakh” means “May the One who blessed,” the first words of the prayer which goes on to list our patriarchs and matriarchs, and ask for such a blessing for the ones at hand. It dates back at least to the Mahzor Vitry, written by Simhah ben Samuel of Vitry, who died before 1105 CE. (More about the Mahzor Vitry at this link.)
On days when we read the Torah, even on Shabbat when we generally do not petition God for anything, we pause in the Torah Service for this prayer asking for a rapid and complete healing of body and soul of those who are ailing. Often we read from a prepared list of our friends and loved ones to remind ourselves and God that they are in need. We ask for healing for all who need it, specifically those listed, those within our community, and all those suffering. Many congregations sing the song composed by Debbie Friedman, which incorporates some of the Hebrew and some English. (Your correspondent often sends a link to that song to those who are praying for healing.)
We list names in the Mi Sheberakh prayer in Hebrew in an unusual way. A person usually would be addressed in Hebrew (called to the Torah, for instance) as, say, “Avraham Yitzhak ben Meyer v’Sarah,” which is “Abraham Isaac son of Meyer and Sarah” or “Hannah Nekha bat Yehudah v’Rezabella,” which is “Hannah Nekha daughter of Judah and Rosabelle.” Some from the “old school” use only the father’s name, “Avraham Yitzhak ben Meyer,” but many of us are trying nowadays to be inclusive of our mothers as well.
For a Mi Sheberakh, though, we list our loved ones as, for instance, “Avraham Yitzhak ben Sarah,” using only his mother’s name, or “Hannah Nekha bat Rezabella.” This is believed to date back all the way to King David, who asked God for help saying, “I am Your servant, the son of Your maidservant.” Another theory of its origin is more direct, though a bit chauvinistic, that our mothers are the ones who care for us, who tend to us when we are in need, and thus we should use their names when we need loving attention.
Some also say that we can always be sure of a person’s lineage through his/her mother, thus the person is clearly identified that way. On the other hand, though, sometimes people wish to list names in a Mi Sheberakh list as pseudonyms, under the superstition that if we pray with the real name, the Angel of Death will see that the person is ailing and take the person sooner.
Sending positive thoughts, praying, and making active calls to help those who are ailing to heal in body and spirit is present in most religions. However we mobilize that, it seems to be effective.