Do doors provide any cover at all

Since no one (other than Firaxis) can know for sure, here's my interpretation of your picture:

The soldier you're trying to target isn't standing in the open door, but next to it. He's standing in the same line as your soldier, and the full-cover-box you can see behind the doorway.

I think it's that specific box that is blocking your LOS. Even if we consider that your soldier sidesteps (so let's assume she's standing one tile to her left); it's possible that the slight elevation of the train cart combined with the angle of the box (relative to how your unit would see the enemy soldier) leads the game to decide it's not in LOS.

That being said, this is just a guess. I remember being in similar situation and seeing my target. The only thing different here is that box, which is why I'm thinking that's the reason.

Edit
For those who argue that the enemy (model) is in sight of the soldier, therefore it should be targetable, keep in mind that the game calculates based on the tile a unit is on, not the actual visibility of their character model.

I find that units in cover really cling to the cover, or try to pop out their heads, and it throws off your vision on where the tile is located. If you look at OP's picture, you'll see how much difference there is between the enemy's body and the actual center of the tile they're standing on.

tl;dr: It's the average amount of defense your units were receiving from cover at the end of each turn.

At the end of each of your turns, the game records how many living soldiers you have, and what type of cover each of your units is in (none, low/half, or standing/full). These are added and stored as CoverCount and CoverTotal respectively. For CoverTotal, each type counts as follows:

• No cover - 0
• Low/half cover - 1
• Standing/full cover - 2

At the end of the mission there's a fairly simple calculation:

CoverPercentage = CoverTotal * 20 / CoverCount

This represents the fact that low cover adds 20 defense, and high cover adds 40.

Note that CoverTotal is added to based on the best possible cover for your soldier. Your soldier can be flanked by 6 aliens, but as long as they're standing next to a full cover tile, they're going to count as full cover for the purposes of this calculation.