Single-stage furnaces have only one setting: full blast. They use full fuel all the time, no matter the temperature outside. Two-stage furnaces change their output depending on how cold it is. In freezing temperatures they run at full capacity, two stages. If it's a little chilly out, they'll just run one stage, saving you fuel and money.
The price difference between the two operating systems is a few hundred dollars. It's money well spent — if your budget allows it. Two-stage furnaces do a better job of removing cold spots and save you more money in heating costs.