Steps to debug Background task
For debugging back-ground task, there are few changes required to above program and FM which I have already created (Pre-requisite Points for back-ground task)
Running a module in back-ground task means assigning the module to separate LUW.
It can be run parallel and is an asynchronous process.
Changes required are mentioned below. 
To debug our background task we need to switch on Do not process in debugging mode as shown below
Once we execute our program in SE38, FM will get execute in background task and it will be assigned to a separate LUW.We can see this LUW registered in t-code SM58 and execute, debug and delete manually.
If we do not check above check box, then LUW gets execute automatically and immediately based on attribute settings at FM level. It does not wait for user to manually execute the same.
Before executing, let’s check in SM58. 
Now let’s execute the program and check the same step by step.
/H to switch on system debug and so that we can mark Do Not Process check box
Put the cursor on below record and follow the path shown below to debug.
After above execution process, corresponding record from SM58 will be deleted.
SM58 can be explored more to gain knowledge about different other remote debugging options.