Board Control is a common concept among more popular card games like Hearthstone and Magic the Gathering; however, the same concept can be applied to Deck Heroes as well. The term "Board Control" refers to having more creatures (or more powerful creatures) on the field than your opponent.
What is Board Control and why is it beneficial? Edit
As stated above, board control is when you have control over the field, either by having more creatures, or by having more powerful creatures than you opponent. Being in this position is incredibly advantageous, because it allows your creatures and hero to work together to deal even more damage to the enemy creatures and/or hero. Also, it gives your utility creatures (my Queen Temptress with Retreat, in the above example) more defense from offensive enemy creatures. Once you have gained board control, it is hard to lose it. Likewise, once you have lost it, it can be hard to get it back.
How can I more easily gain Board Control? Edit
Board control is obviously gained through killing off the enemy creatures; however, there are many methods to go about doing that.
Sweeping Blow Edit
Sweeping Blow is an ability which allows a creature to hit 3 creatures at once, instead of just 1. This essentially triples a creature's damage output, making it very good at clearing the enemy's side of the field. Creatures with Sweeping Blow include but aren't limited to: Sea Wizard, Ridge Hunter, Graboid, and Fafnir.
"Area of Effect" spells are spells that hit a large amount of creatures (normally 5 or more). Pyre (from Flame Brave or Blossoms) and Tempest (from Sea Wizard or Tidal Siren) are great examples of AoE spells, since they hit every enemy creature, and can be very devastating if not blocked by Immunity.
A very popular method in the current high level meta is to use Queen Temptresses melded with Retreat. Retreat allows the creature to send the creature in front of it back to it's owner's deck, allowing your creature a direct shot at the enemy hero. This allows the Queen Temptress the ability to more easily steal rage from the enemy hero and give it to your own. Although this is the most popular usage of Retreat, a normal Archdeva or Revenant will work as well.
Literally meaning "sovereignty, or control", this is Taskmistress' hero skill. If you are lucky enough to have her at a high level, then you can gain massive amounts of board control with her hero skill, which sends enemy creatures back to your opponent's hand, while cloning them for use on your side of the field.
Meaning "to cause great suffering to", this is Spirit Arbiter's hero skill. Scourge heavily damages 1, 2, or 3 enemy creatures (depending on her level), increasing her rage if she doesn't kill anything, and has a chance to remove the creatures from play if she does kill them.
How can I prevent myself from losing it? Edit
Losing board control can be very bad if your opponent is more powerful than you, so you're going to want to do everything that you can from losing it.
The most obvious way to prevent your creatures from dying (and thus giving your opponent more control) is by healing them, either through Mass Heal, Restoration, or using hero skills like Prayer and Earth's Embrace.
Frost Armor, Dodge, Maji Shield, and Immunity Edit
Making your creatures less susceptible to damage is also a very obvious way to keep your creatures on the field. The most Frost Armor and Immunity the better. Stoneskin is also decent, since it prevents your creature from being Instakilled or Retreated.
Kill Enemy Creatures Quickly Edit
Don't give your enemy's creatures a chance to stay on the field for more than a few turns. The longer that they stay on the field, the more damage they can do.