Demand Curve Equation Explanation
In this demand curve, $a=6$ means that the autonomous demand for this good is of 6 units. That is, if the market price of that good was $0$, then people would demand 6 units. 

It is reasonable to think that a positive income shock, or a shift in preferences making this good more desirable would make $a$ higher. I don't think there's any deeper meaning here, just that a downward sloping demand curve requires a positive intercept or else quantity demanded would be negative at any price $P$.