The history behind the date of Mother’s day in the USA is pretty simple. It’s on the second Sunday of May because President Woodrow Wilson decided to make it an official national holiday. This was decided in 1914, and it stuck. No one has ever decided not to celebrate on the designated national holiday if they wanted to celebrate.
However, as the previous answer has pointed out, the date for Mother’s day is different depending on where you want to celebrate it. A lot of countries have something similar in nature to what is known as Mother’s day in the USA. Not all of them are celebrated in May, and not all of them will be on the second week of a month.
It is celebrated on different days according to which of the 40 countries where it is celebrated that you happen to live in.
In US it's the seconday Sunday in May because Woodrow Wilson designated that in 1914, a national holiday to celebrate mothers and motherhood. The date is the same in Australia, but in UK it's always 3 weeks before Easter.