One reason is it makes your mind active instead of passive. People who are curious about things will ask questions about it and they will do it until they find out the answer. Just think of your brain like it is a muscle, when you exercise your brain, your brain becomes stronger and stronger. Another reason is it opens up a new world and possibilities for man kind. For example, before Edison invented light bulb, we have to use candle to be able to see at night. But Edison sacrificed his time to make our life easier. He tried hundreds and thousands of times and he never give up because he believes one day he will succeed. The process of finding the answer may be painful and frustrated, but all of the hard work will pay off one day.
Do you think curiosity is like the on and off button for new inventions? And tell me what are you curious about at this moment?
If you are interesting in the topic you can try the link below
http://www.beswick.info/psychres/curiosityintro.htm