Your handlebars are actually two levers connected in the middle. The place where a lever is attached is called the fulcrum of the lever, and the fulcrum for your handlebars is the vertical tube on the front of the bike, called the head tube. The farther your hands are from the head tube, the longer the lever is. And longer levers require less force to move them. That's why it's easier to steer when your hands are far apart. When your hands are close to the head tube, you are making a short lever (or two of them, one for each hand), and that requires more force to move it.

You don't get something for nothing, though. When you make a lever longer, you don't have to push it as hard, but you have to push it through a longer distance. That's why we don't make handlebars that are 4 feet long... they'd be super easy to turn, but you'd have to move your arms 3-5 feet to make a turn!