To answer this question, we need to understand something about electricity. There is a formula that says V = I R, (voltage V equals current I times resistance R). It is from this formula that we can explain your question. The voltage V represents power, the current I represents current, and the R represents the resistance that any body offers to the flow of current.
First of all, the current running through the body of a bird standing on the telephone or power cables is too small to hurt the bird. This is because the bird offers a high resistance to the current flowing through its body, so almost all the current passes through the cables instead of the bird. The same situation happens with the human body. Unless the body is wet, it always offers a high resistance to the current.
In order for the current to flow through the birds body, it needs some voltage across the bird (which offers some resistance R). This voltage across the bird is very small, even though the voltage passing through the cables can be several hundred thousand volts. The reason is that the bird standing on the high-tension cable has both its feet placed firmly on the same wire close together, and then the voltage between the legs of the bird is very small.
This is the simplest way to answer your question. There are still more electrical concepts to discuss here in order to understand that there are certain circumstances under which the bird would be severely damaged, but this is something different.
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