In this situation it means that the ground (or water) near a downed power line is charged, but the voltage drops quickly as you get further from the conductor (that's the potential gradient).
It can ruin your day if you walk towards or away from it, because your feet might bridge two areas of ground that have a 10kV difference.
Your body being a bag of salty water makes a much better conductor than dirt, so the voltage takes the path of least resistance.
The safest advise is don't try to traverse the ground in that situation at all. However, if you must, the advice is to hop with your feet together or shuffle with very small steps (with the understanding that if you fall you're almost certainly going to fry).
Minor quibble: This implies that electricity only takes the path of least resistance. Electricity actually takes all available paths in inverse proportion to the impedance of the paths. This is why grounding rods don't keep you from being electrocuted. I'm looking at you, sketchy lamp-post.
Good clarification. When I was a kid I found out that standing on the edge of the kitchen sink and touching the pull chain on the lamp in the soffit overhead would 'tickle'. I was so proud when I told mom and dad! :P
Bad idea. If you slip even once, suddenly you don't have "just" the 1m of an ordinary step but 1.5 or 2m... and the longer, the greater the voltage gradient.
It can ruin your day if you walk towards or away from it, because your feet might bridge two areas of ground that have a 10kV difference. Your body being a bag of salty water makes a much better conductor than dirt, so the voltage takes the path of least resistance.
The safest advise is don't try to traverse the ground in that situation at all. However, if you must, the advice is to hop with your feet together or shuffle with very small steps (with the understanding that if you fall you're almost certainly going to fry).