Line of sight determines what a model can 'see'. Many situations call for you to determine whether or not a model has line of sight. A model normally needs line of sight whenever it wishes to attack an enemy, whether with sword, spell or bow.
Line of sight literally represents your warriors' view of the enemy – they must be able to see their foe through, under or over the battlefield terrain, and other models (friendly or enemy).
For one model to have line of sight to another, you must be able to trace an unblocked line from its eyes to any part of the body (i.e. the head, torso, arms or legs) of the target.
Sometimes, all that will be visible of a model is a weapon, banner or other ornament he is carrying. In these cases, the model is not visible. Similarly, we ignore wings and tails, even though they are technically part of a model's body. These rules are intended to ensure that models don't get penalised for having impressive banners, swords, and so on.
Naturally, you can't ask your models what they can see – they're plastic and metal, so a reply will be some considerable time in coming – therefore you'll have to work it out on their behalf. In many cases, this will be obvious – if there's a hill or building in the way, the enemy might be blatantly out of sight. In other cases, two units will be clearly in view of each other as there is nothing at all in the way. On those other occasions where it's not obvious whether or not one unit can see another, the player will have to stoop over the battlefield for a 'model's eye view'. This means getting down to the level of your warriors, taking in the battlefield from their perspective to 'see what they can see'.