Your lap is the top of your thighs when you sit down, where your cat might sit. Lap can also refer to a trip around a racetrack, or to the act of overtaking a competitor by a lap.
Lap is associated with a number of idioms. If something "falls into your lap," you have gotten something without making much effort. For example, maybe you discovered a rare fossil in your yard while looking for your lost baseball. If you sold that fossil for a lot of money, you may find yourself now "sitting in the lap of luxury." That’s a wonderful place to be!