back is the place where the plug fits into the bath is suppose to block bigger objects from going down the drain, however as a security measure other forms of debris and hair usually get tangled preventing it from causing bigger blockages some where else down the drain. This exact problem once happened in my bath. I used an end of a coat hanger to remove the hair.
Remember to always use a pair of good quality plastic gloves , you never know what objects could be in places which you can't see. Be persistent as many years of build-up does not go just in a few seconds. If you find that their is other gunk that you can't get to , remove the screw to the strainer, don't loose the screw down the drain. Next is to clean the "P-TRAP". With the coat hanger remove all what you can see. Next you need to put back the strainer and fill up the bath
with warm water and then release the plug allowing a flush of the pipes. A drain cleaner can also be used , be sure to follow the instruction as they are abrasive. Use always skin protection and eye protection. Okay now you have got the water flowing freely again, in some other cases you may have to use a plunger for problems you can't see. The first step is to have enough water in the bath to cover the bottom of the plunger next-page