"In an American context, mixed race people passing for white would tell others that their darker coloring was due to a Black Dutch or Black Irish ancestry, rather than an African or American Indian grandparent."
It kept them from being listed as "mulatto" or "colored" on the census, which could and often did lead to being run out of the county or having your land seized, in Ol' Virginny at least.
It was not uncommon for mixed race Virginians and other Southerners to migrate to the North to "pass" as white. A classic example of passing for white was in the case of the descendants of Sally Hemmings with either Thomas Jefferson or a relative of the third President. They emigrated to Ohio and developed a "white" identity. There were rumors that Warren Harding had mixed race relatives on his mother's side who had moved from Virginia to Ohio. Many blacks believed that Babe Ruth was partially African American. It is also possible that J. Edgar Hoover had black ancestry through his mother's lineage.