Father's Day is the corresponding day for fathers and fatherhood.
Celebrations of mothers and motherhood occur throughout the world; many of these can be traced back to ancient festivals, like the Greek cult to Cybele or the Roman festival of Hilaria. The modern US-celebration of Mother's Day is not directly related to these.
One of the early calls to celebrate a Mother's Day in the United States was the "Mother's Day Proclamation" by Julia Ward Howe. Written in 1870, it was a pacifist reaction to the carnage of the American Civil War and the Franco-Prussian War. The Proclamation was tied to Howe's feminist belief that women had a responsibility to shape their societies at the political level.
In the years after the Mother's Day Proclamation, Ann Jarvis founded five Mothers' Day Work Clubs to improve sanitary and health conditions. In 1907, two years after Ann Jarvis' death, her daughter Anna Jarvis held a memorial for her mother and began a campaign to make "Mother's Day" a recognized holiday in the US. Although she was successful in 1914, she was already disappointed with its commercialization by the 1920s.
As the US holiday was adopted by other countries and cultures, the date was changed to fit already existing celebrations honoring motherhood, like Mothering Sunday in the UK or, in Greece, the Orthodox celebration of the presentation of Jesus to the temple (February 2). In some countries it was changed to dates that were significant to the majority religion, like the Virgin Mary day in Catholic countries, or the birthday of the daughter of the Prophet Muhammad in Islamic countries. Other countries changed it to historical dates, like Bolivia using the date of a certain battle where women participated. See the "International history and traditions" section for the complete list.
Note: Countries that celebrate the International Women's Day instead of Mother's Day are marked with a dagger