Why can birds sit on high-voltage wires and not get hurt?

There is much less resistance for electricity in the high voltage line compared with the bird. The electric field of the powerline remains in the wire, it does not extend through the bird as there is no easily conducting material for current to move through the bird.

For the bird to be electrocuted a current must flow. A current will flow through the bird only if there is a potential difference. Although, the live wire may have a high potential (many thousands of volts) both the bird's feet are at the same potential when on the wire and since there is no difference in potential between the feet no current can flow and the bird is safe. In contrast, if the bird were to put one of it feet on another wire at a different potential (say earth at zero volts) then there now exists a potential difference for the current to flow and the bird will be electrocuted.