Hedgehog formations are used by shooty armies to defeat the balanced line, or horde army. Hedgehog formations tend to be tightly packed fire bases packed in a corner or an easily defendable position on the side of a board.
Hedgehog strategies are usually are used with shooty armies, but can also be used by hth armies that are expecting to go up against a maxed out drop pod assault army. The concept is to create a localized fire base in a corner and remove any speed superiority the enemy may have and create a concentrated point of fire power. It also forces any units deployed on a far flank to move a much further distance to mount an assault, allowing the shooty army to divide the army up by shooting the closest unit first and further away units on subsequent turns. A good tactic with this formation is to deploy satellite speed bump units. These units can be fed to the enemy to further stagger his approach, giving you more time to pick your opponent apart piecemeal.
The strength of the hedgehog lies in its ability to deny the other army any localized superiority in shooting or hth. The game is played on the shooty armies' terms. Deployment is very important with this formation. If you deploy second you can at least negate one heavy as you can deploy everything in the far corner. It tends to be a tough formation to pull off without tipping your hat too early.
The hedgehog tends to be an all eggs-in-one-basket play. You are betting that you will damage the other army enough that you can handle anything that makes it to hth. If you don't do enough damage, the first combat kills your line of sight, and you're done. Other weaknesses include being packed together and vulnerable to ordinance, as well as being ill-prepared to win a mission with an objective other than wiping out your opponent.
The most common variation is the castle formation, otherwise known as the empty center formation. This formation in it's most basic for is a hedgehog in either corner. This forces an enemy to either divide there force to kill each hedgehog or mass to one side. If they mass to one side they will likely kill off half your army after taking serious casualties, they have to go all the way to the far corner to get the other half of the armies, taking casualties along the way. This formation works especially well with two pieces of indirect ordinance that can cover each other from across the board and denying your opponent the choice to kill one side and hide.
I find hedgehogs are the answer to horde armies for shooting armies. It gives shooty armies the ability to divide and conquer, and it is easy to set up the formation as a horde army usually starts running out of space in its deployment zone.
The castle formation tends to work better against elite armies as they don't have as many models/units. The castle can be mobbed by a horde as the distance of separation breaks down, because horde armies tend to be spread across the entire board. Against Elite armies they need to stay closely packed to support each other to gain localized superiority. Deploying two pieces of an elite army at each corner is an easy way to hand your opponent the game.