When I worked at the airport in Niles, MI, there was an old dude there that had a Cub with a STOL kit. He came out on a very windy day and said, "Watch this!". He taxied out to the start of the runway, ran up his engine, rolled about 50 feet forward and it popped up into the air. He went up about a hundred feet, drifted backwards about a hundred feet and slowly brought it forward and down exactly at the start of the runway. He flew backwards. In relation to the ground, he went forward 50 feet, backwards about a hundred feet, and then forward about 50 feet again. His airspeed said he was going 40 miles an hour, but he went nowhere.
Now, had this been a calm day, he would have had to move forward up to 40 MPH in relation to the ground, before he would have been moving through the air at 40MPH, the magic number he needed for lift. He has to overcome the rolling friction with the ground first, then gain the airspeed. If he isn't going anywhere in relation to the ground first, he can't go anywhere in relation to a point in the calm air, either.
Here's another example from that same airport...
A guy came out with his weiner dog. The weiner dog was named Snoopy and was wearing a leather pilots helmet like a WWI ace. They hopped into his airplane and tried to taxi out of the flight line. He had forgotten to untie his tail from the steel cable in the grass. He gave it lots of power. He pulled about a hundred feet of cable behind him, ripping out anchor after anchor. You would think that with a cable anchored to the ground a hundred feet behind him and his engine generating max thrust that he could just pull back on the stick and pop into the air. Well, he couldn't because he had zero airspeed. The same thing would happen with an airplane on a treadmill. He has to get up some ground speed in relation to a fixed point before he can get up some airspeed. I threw in the weiner dog part because he was cute. He was disappointed that they couldn't go for a ride that day.