What is EXIF? It stands for “exchangeable image file format” and it contains information such as shutter speed, ISO speed, and various other information (including, if the device has a GPS, the location of the photo). 
If you are posting this information to the internet, you could be uploading this information with the picture. For example, if you post a picture of your house and sometime later you post you are on vacation. This would be all the information a criminal would need to gain access to your house.