Temperature is a measure of the kinetic energy (movement) of the particles in a substance. Theoretically, absolute zero is the temperature at which everything stops moving, making it the lowest possible temperature.
People first got the idea from looking at temperature vs. volume graphs of gasses. At constant pressure, they are directly proportional and form a straight line. Imagine a graph with a y intercept of 5 liters at 0 degrees celsius. As you decrease temperature into the negatives, the volume will decrease linearly until a certain point. What happens at the x intercept, with zero volume? The answer is the same for all gases and is called absolute zero. If you extend the line enough, you get to the lowest temperature possible