Board control is an interesting concept and can be achieved in a number of ways. This can by through having dangerous models or by moving models around or limiting enemy movement.
Certain models exude danger: the Deathjack, Mulg, Beast-09. You'll notice that these are mostly large models that have a big presence when you put them on the table. They're designed this way and most players can instantly identify the threat something like Mulg will bring to the table. This presence is further enhanced by the model's rules. Everyone knows that the Deathjack or Mulg or a Warpwolf Stalker can ruin just about any single model in the game, so you don't want to put your models on the receiving end of their attacks. Now we're seeing where the board control comes in.
When you put down a model, it exerts a certain radius of 'threat'. Anything entering this 'threat' becomes a valid target. The more threatening or destructive a model is, the more board control it exerts on your opponent. No one in their right mind will place a caster within 14" of Mulg with eDoomshaper unless they can absolutely guarantee (and I really mean guarantee) their caster cannot be attacked/killed. So utilizing this theory of threat you effectively control the board within your model's threat range.
What happens when multiple competing threat ranges overlap? So my Mulg+eDoomshaper combo can threaten 14", but your Molik Karn+eMakeda can go 15", that's when I surrender the board control to my opponent unless I can nullify their assault. Whomever has the longer threat range is exerting more board control on that area of the board than their opponent. Certain factors such as attack power come into play here too though, my ARM 21 Mulg is going to laugh at your POW 10 infantry even though they exert a larger threat range. Because I effectively nullify your assault, that part of the board is really mine.
Certain feats and abilities change the way board control works. eDeneghra's feat instantly drops your opponent's board control to nothing as long as they can't move, so you now control the entire board except where models are physically placed and their respective melee ranges. This harkens back to the idea that threat range is the greatest factor for board control. Look at the way Pygmy Burrowers works, because my Burrowers nullify your threat by digging and do horrific damage when they surface, they exert a good degree board control.
It's worth talking about abilities that literally effect the board: things like suppressing fire or pillars of salt. These are usually templates that either stop your opponent moving through or limit where they can move. You are in effect channeling your opponent's army in a more direct fashion than using threat range by saying "you may not move here" with your templates. Of course this is cancelled if the opponent can ignore whatever type of template you put down but you get the idea on how it works.
So what can you do with board control? Well, the first thing you can do if you have more board control than your opponent is dictate where combat will happen. Denial casters typically support this sort of play, though some casters enter a sub-genre of denial most people would call control: casters such as Rahn or eKrueger fit into this category. Once you can dictate where combat will happen, it becomes a matter of when it will happen. Once you control the where and the when then you pretty much have the game in the bag unless the dice let you down.