Yes, airplanes do fly at night. There are overnight flights, or what are called red-eye flights. The vast demand for flights and the many people that travel each day have raised the demand for more airplanes to be in operation. There are also time zones to take into account. By flying at night, it is possible for some to sleep and then adjust their bodies to their locations when they arrive.
Freight planes also travel at night, bringing packages, mail, and closer to their destinations. Each day, there are over 6,000 airplanes operating at any given time. These can range from domestic flights to overseas locations. If airplanes only operated during daylight hours, there would be an increased risk of planes overlapping in the air, which could cause many more accidents.
For safety reasons, having planes fly overnight decreases the risk of having too many aircraft operating at one time, while allowing air traffic controllers to better monitor the planes that are in operation.