The actual definition: White Dominions are colonies in which European settlers made up the overwhelming majority of the population; small numbers of of native inhabitants were typically reduced by disease and wars of conquest; typical of British holdings in North America and Australia with growing independence in the 19th century.
In more common usage: During the imperialistic era many Brits went around the world capturing land, controlling the people that lived there. In instances like Australia and North America we see that when the British came over many natives were treated considerably cruelly in order to keep control.