The Lord God had created people to have dominion over all animals (Genesis 1:26). By the woman's “sitting” on this seven-headed, ten-horned animal, she displays that she exercises her dominion over it; she is the beast’s mistress—and hence the beast her servant doing her bidding (think of the relationship between a horse and its rider). This point is particularly significant when we realize who/what this beast is.
3 And he carried me away in the Spirit into a wilderness, and I saw a woman sitting on a scarlet beast that was full of blasphemous names, and it had seven heads and ten horns.