Current flow with a Diode
Conventional current flows through the circuit from the positive terminal to the negative. It's called 'conventional' because that's the convention we have all decided to use. It was standard before it was known that electrons have a negative charge and flow in the opposite direction. It doesn't matter which we use from a circuit analysis point of view, provided we all agree to use the same one- that one is that current flows from positive to negative. 

The diode's schematic symbol has the 'arrow' in the direction of current flow when forward biased. 

PS The link given by an above comment from @Tyler is amusing, and also makes reference to this xkcd comic.