The answer lies in how electricity functions.
Have you ever looked at birds sitting unruffled on power lines and wondered what magical ability they have to pull off such a feat? Well, the answer is not magic but rather science.
Electrical current consists of moving electrons that travel from a power station to their destinations where they provide electricity and back into the ground. This process creates a closed loop necessary for electricity to flow.
There's one more thing that electrons need to travel and that is a difference in electrical potential. Electrons move from one electrical potential to a lower one. However, when birds sit on wires, they do so with both their feet on the same spot, therefore, the same electrical potential. As such, electrons have no reason to move through them.
Should the birds decide to touch a different wire with a different electrical potential, then they would be in trouble! That's why it is dangerous for birds to sit on the wood pool supporting the wires. If they were to do this and also touch an electrical wire, then they would be in trouble once more.
It is safe to say that humans should avoid touching wires at all costs. Unlike birds, since we are in constant contact with the ground (a lower potential), we make great electrical conductors, which means we can be zapped good.