Have a look at the following phase diagram:
(Diagram from this web site)
I've drawn the vertical green line to mark 15% ethanol by mass, which is about the maximum you can expect from wine. The boiling point of the mixture is the point where the green line crosses the blue line so it's about 90ºC (the diagram is approximate, so don't read it too literally). The composition of the vapour is given by the pink line, so follow the horizontal green line over until it hits the pink line, and we see the vapour is about 40% by mass of ethanol.
So when you first start distilling your wine you'll end up with a distillate that's about 40% ethanol. To get the ethanol more concentrated you would have to take the distillate, put it back into the still and distill it again.
If you leave the wine in the still the ethanol content in the liquid will fall as ethanol is removed. Consequently the boiling point will rise and the ethanol content of the distillate will progressively fall. For any water/ethanol proportion you can read off the boiling point and distillate composition from the phase diagram.
For anyone willing to read past the tl;dr limit, note that the blue line reaches a minimum value at 95.6% ethanol. This is known as the eutectic point. At this point the composition of the vapour and the liquid are identical, so you cannot concentrate the ethanol any further by repeated distillation. To get the ethanol any more concentrated you have to add a third component to shift the eutectic point. This process is called azeotropic distillation and in the ethanol/water system benzene is used.