Background data is data that is used by apps that run in the background. Typically these are apps that you can't technically stop from running unless tou are willing to take a few extra steps, and even then, not all apps can be stopped from background processing. Another part of this would be things like system or social media apps. When you recieve notifications from these types of apps even after closing them, it means they are programmed to run in the background in case they need to notify you. On top of all that, yes, background processes or data usage will cause battery usage, but not very much. If a smart phone is on, wheather it's locked or not, it is constantly doing something. The OS it's self is always working. If it wasn't, you wouldn't have a functioning device.
Side-note:
Your carrier will also be constantly bombarding your device with data usage signals so long as you are in range of service. The only way to completely disable background data usage, would be to enable airplane mode.