Why is it that for a source of emf, current flows from lower to higher potential? I'm quite confused about this actually! In fact, I had always thought current flows from a region of higher potential to a lower one. Does it have anything to do with the fact that it's a source of emf instead? What significance does that have?
 A: Within a source of emf like a battery a chemical reaction occurs which moves the mobile charge carriers from a region where they have low electric potential energy to a region where they have a higher electric potential energy.
If the charge carriers are positive that is taking those positive charge carriers from the negative terminal of the battery to the positive terminal whereas if the charge carriers are negative that is taking those negative charge carriers from the positive terminal of the battery to the negative terminal.
The source of emf can be thought of as a pump which raises the electric potential energy of the mobile charges at the expense of work being done which in the case of the battery is the chemical reaction whereas for a water pump it might be you turning a handle.
Question:(from Anurag Kar)
In short should we assume that the terminal where the positive or negative charges are going into has higher potential than the place they are in now??
A: I suspect that your confusion is caused by the difference between conventional current and the flow of electrons.
Conventionally the direction of a current is the direction in which +ve charges move, and this direction is from higher potential (more +ve) to lower potential (less +ve).  However, this convention was chosen historically before we knew what the charge carriers are.  We now know that in metals current is a flow of -ve charges (electrons).  The flow of electrons is from lower potential (more -ve) to higher potential (less -ve = more +ve).    
