The temperature where all molecular motion has stopped is referred to as absolute zero, and it is considered as the lowest possible temperature ergo "absolute". Despite what the article title reads, absolute zero is at zero Kelvin, making the Kelvin scale an absolute temperature scale, which is equal to -273.15 degrees Celsius (where the confusion with the article title comes from) or -459.67 degrees Fahrenheit.
Of course, as far as human knowledge goes, such a temperature has never been reached, but people have gotten extremely close (450 pK). That being said, how could people claim that as a minimum temperature? This can be attributed to many scientists such as Galileo, Robert Boyle, and Guillaume Amontons. The last of which was the first to experimentally attempt to locate this point. In 1703, he used an air-thermometer to determine that absolute zero was about -240 degrees Celsius, which is notably close considering that he did this over three hundred years ago. Later (about 1780) Johann Heinrich Lambert did an extremely similar experiment and came up with an very close prediction of -270 degrees Celsius. But it was Lord Kelvin who determined our modern-day representation of absolute zero by using the laws of thermodynamics.
A common first year chemistry lab can simulate this by using Charles's Law. In short, Charles's Law states that, ideally, a gas at constant pressure would have a constant ratio between the volume and absolute temperature. By measuring the temperature and volume of a gas, typically just air to be easy, at two different temperatures, absolute zero can be extrapolated back to the zero volume using the principle from Charles's Law.
Who cares? Mostly just scientists. Unless someone needs to be using ideal gas equations, calculating Gibb's Free Energy, or other like things, a normal Celsius or Fahrenheit scale will work just fine, but there is some very important math that is involved in certain sciences that depend on using temperatures scales based off of absolute zero.