What the Structures mean...

  After you have worked out the point values for each battle, but before you build your army, you and your opponent will compare tiles/assets to see if you have battle bonuses. Compare the points you have against the points your opponent has. Refer to the charts below for detailed army specific assets.

• Power Stations modify the die for Picking the table edge, Who goes first and Reserves!
• Command Bastions give out Universal Rules, so Howling Banshees with Furious Charge could be on a table against you...or Sternguard with Feel No Pain...or Melta Vets with Tank Hunter.
• Shield generator is for the end of the month roll to resist taking a tile.  So you are adjacent to an imperial guard players Hive city tile and you have beaten him in an omega level cites of death game.  End of the month comes around an you roll to take the tile,  Being adjacent is a 3+, but there is a -5 from the Shield generator, and another -1 for it being a Hive City, so you will need a 9+ to take the tile.
• Manufactorum, simply adds to the point you build your army with.  If you have 3 times the Factory points as your opponent, you get an extra 150 to build with.
• Tiles.  This work opposite of how you would think.  The player with the fewer amount of tiles gets the extra points.  This is to because the player with more tiles has to spread his forces out more to cover all his tiles. 
• The maximum bonus for Power Stations, Command Bastions and Manufactorums is 3x.  So if a player has no power stations, and their opponent has one power station, their bonus is the 3x row on the chart below.

There are two ways to add points to your army build.  One through Manufactorums, Two through having fewer tiles than your opponent.  Now spending those extra points are handled in a slightly different way...

Spending bonus points
Bonus points can be used to either add units to the player's army list, to allow the player to take mercenary units from a different list, or to ask for help from another player in the form of allied units.  For example, a Space Marine player with a bonus of 150 points could either add 150 points to his army, or use 150 points worth of units chosen from another army list (Imperial Guard, for example, or Eldar), or ask another allied player to help out with 150 points worth of allied units.

Mercenary and allied units take up force organization slots on the player's main army. In effect the units count as part of your army, even though they may have been chosen from another army list or lent to you by another player. For example, if you took a mercenary Heavy Support unit, then it would take up one of your Heavy Support slots. Note that any further restrictions that apply to taking mercenary or allied units in their own army list are waived.

Design Note: Mercenary units are included to allow players to use models from other armies in their collection. It's also a cool way of starting to collect a new army.  Allied units, on the other hand, allow you to include models from another player's army with your own - they can be controlled by you, but really they should be commanded by your ally!