"Hanging Chad" became popularized from the 2000
presidential race between
George W. Bush and Al Gore.
A "chad" is the fragments of paper left over when you punch a hole in a card. Voters in Florida at the time used Votomatic style punched card ballots. So a "hanging chad" is when you punch a hole in the card, and it doesn't punch the whole way leaving a little piece dangling. A "pregnant chad" is when you attempt to punch a hole, but it just leaves a bulge and doesn't actually punch through.
The controversy came about when "hanging chads" and "pregnant chads" weren't counted by the machine. People's votes weren't counted.
Imagine if you take those tests where you have to fill out the circle completely with a
number 2 pencil. But you didn't totally fill the circle out and your answer was marked wrong.