It is celebrated on Shevat 30, which falls anywhere between January 30 and March 1. It was set to the same day as the birthday of Henrietta Szold. Henrietta had no biological children, but her organization Youth Aliyah rescued many Jewish children from Nazi Germany and took care of them, and she also fought for several rights of Jewish children. She is considered the "mother" of all those children, and that's why her birthday was set as Mother's Day (יוֹם הָאֵם, yom ha'em). It has evolved over time, becoming a celebration of mutual love inside the family and it's called Family Day (יוֹם הַמִשְּפָּחָה, yom hamishpacha). It's only celebrated by children at kindergartens, there are no longer mutual gifts among members of the family, and there is no longer any commercialization of the celebration. It's not an official holiday either.
Israeli Arabs (about 20% of the population) celebrate Mother's Day on 21 March, similar to other Arab countries.