Line of Sight
Line of Sight refers to the ability of a character to see another square. Of course, you as the player can view the whole board from above. Your adventurers' vision, though, will be blocked by walls, trees, and other clutter. Why does this matter? Well, if they can't see a square, then they can't aim their weapons or magic. Nearly every active ability in the game requires that the character playing a card be able to see a valid target.
Calculating Line of Sight
Calculating line of sight is simple. Choose any two squares on the board, and draw a line between their centers. As long as that line does not cross any Blocking Terrain (which is distinguished on the board with a thick black outline), those two squares have line of sight with each other. That's it. Blocking terrain is the only limit on how far your characters can see across the field of battle.
You can see in the diagram that all the squares marked 'A' have line of sight with the character standing at the blue circle. One is a straight line to an adjacent square, that's pretty obvious. Another is a diagonal line that goes past the corner of blocking terrain but does not cross it. The final marked square up at the top has a line that crosses an "unseen" square, but not Blocking Terrain, so the line of sight is valid.
The squares marked 'B' do not have line of sight with the character's square. One is actually inside Blocking Terrain. The other is on the far side of some Blocking Terrain, so the line of sight fails.
The square marked 'C' has line of sight, but it is slightly different because it is considered to be "behind" the character (who is facing in the direction of the arrow). Front and behind make no difference to line of sight, so long as the line itself is clear. But some cards, most notably Blocks, have special rules that take Facing into consideration. For that reason, when you mouse over any character without a card selected, you will see an overlay for that charcter's "forward" line of sight only.
