Biggest can have many definition -
1. Based on the land size: British Empire was the largest empire in the history with the size of 33.7 mn sq km followed by Mongol empire and Russian empire.
2. Based on the Population: British Empire was the largest even in terms of population with the total population of 450mn in 1940 followed by the Qing dynasty and Russian Empire.
3. Based on the % of population: This could be the most accurate way of comparison, Achaemenid Empire was the largest empire which ruled 44% of world population at its peak followed by Maurya Empire which rules 43% of world (> 50% of world GDP) population at its peak at the time of Ashoka the great. If we consider the vessel states of Maurayan then it cross the 50% of world population of its time making it the largest.