How does current flow? From + to - or vice versa. Why? Please explain.

It depends on what you define as “electricity”.  Do you mean the flow of “electrons” or the flow of “current”?  Because, the history says, the direction of current flow is opposite to the direction of electron flow. 

If electrons are flowing to the right across this screen, then we say that current is flowing to the left.

So, let’s say that the left hand side of this screen is the positive terminal and the right hand side is the negative terminal
                                                +                  -

Electrons will flow towards the opposite charge, as you say.  Its direction is  Right to left
                                       <—-  electrons

But current is the opposite direction.  i.e., Left to right.
                                         —-> current

So current does flow from positive to negative, like our books say. We define electric current to be the opposite direction of electron flow.

The following figures explaims more clearly:

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Naga Ramesh
IIT Kgp - 2005 batch

Current will flow from  +ve to -ve.

Current always flows from higher potential to lower potential.