Now it may not be obvious when you start the game but Terraria has what is known as a Parasitic biome in the form of either the Corruption(purple) or the Crimson(red), a parasitic biome is one that spreads, taints and eventually over takes other biomes in the game turning them. Now pre-hardmode this isn't a major issue as the rate of spread is really slow. But once you trigger hard-mode in the game, you will spawn a second parasitic biome called the Hallow which is a "good" parasitic biome(good as in while it takes over it doesn't do any damage nor changes any non-desert or plains based biomes) and this and your counter parasitic biome corruption/crimson will spread at a accelerated rate and can and will take over your world if not prevented, hallow is less of a threat damage wise but corruption and crimson spread has some nasty effects including ripping large pits, destroying the jungle biome completly, and should it spread to your base it will make your home/town unlivable.

Now there are a few steps you can take, one is to find all Corrupted or Crimson areas and block them off with Holy water which will turn areas hallow(corruption and Crimson can not spread past Hallow unless it is a very small patch of hallow like 1 to 2 blocks worth) this will buy you sometime

Alternatively you can just build a large wooden wall between areas you want to protect such as the jungle from corruption/crimson on both sides from the top to the very bottom but this is time consuming.

But these are mostly preventive measures ultimatly you need to slay one hardmode boss and then head to the underground jungle(which is of course under the surface jungle) and find a pink flower/pink plant and smash it this summons Plantera, kill it and the spread slows down to it pre-hardmode rates. Also once you kill one mechanical hardmode boss(the twins, destroyer, S. Prime) a NPC named the steam punker will move in that will sell a item called the "Clemteminator" which when used with various solutions will turn a infected biome into any biome of your choosing(this is based on what solution you use Dark Blue to turn a Biome into a glowing mushroom biome, Green to purify a corrupted/hallowfied biome back to it's orginal state) this is a bit pricey of a method but money is easy to get in Hardmode.

Corruption, Crimson and Hallow can spread across 3 tiles of non-corruptible materials. Corruption can also use the damaging Corruption Vines to extend the reach.

The way Corruption/Crimson changes the Jungle is by first turning a Mud block into a Dirt block, then spread Corruption/Crimson grass to that block. Note that Mud with blue mushroom grass is immune to this form of corruption.

Just so you know its not back to prehardmode speed after killing plantera.

1.2.0.3:
The spread slows down to 33% of the hardmode speed after killing Plantera. However it will still convert all blocks as hardmode spread would.

I was always curious how Corruption worked and unfortunately I never tried to dig from the top all the way down in a at least 4 tiles radius so theoretically it won't spread, cutting it off so you don't have to deal with it. Is this possible? That way you can create 3 parts in a post-hard mode game: one for normal, one for Corruption/Crimson and one for Hallow.

It's a fairly common tactic if there's a place you wish to keep safe from Corruption/Crimson. Do remember that the corruption vines that grow from corrupted grass also spread Corruption. You should wall off any corrupted grass so that the vines can not spread corruption if you take this approach.

Also worth of note is that smashing a Demon/Crimson Altar has a chance of spawning a single block of Corruption/Crimson or Hallow in an entirely random location. This can bypass any barriers you've created.

for now, it has been said some changes are comming to the Crimson in 1.3 so it's possible that it's going to get nastier in Hardmode and the upcoming Expert mode

To prevent corruption (and hallow) spread to new soil, including preventing spread through brambles, you will need a 5 block wide wall made of any solid brick (not to be confused with "block"), metal or simply the abundant ash blocks from hell.
I'm not sure whether wood works as a wall, considering a corrupted variant of it exists.

Also noteworthy is that when switching to hardmode, even if you previously cleaned your map of all corruption, when killing the Wall of Flesh a new corrupted vein will spawn diagonally upwards to the right from the location of the bosses death, mirrored by a vein of hallow.

It does. I've had these walls up forever (well before corrupted wood was even added to the game) and they haven't converted. Unless they're so old that the game doesn't recognize them as being able to change, heh.

Wood doesn't get corrupted and Ebon/Shadewood does not count as corruption either.

Hay stops the corruption, too, and it's much quicker to collect than wood.

The Corruptor has been nerfed, shortly after the Crimson was introduced. It still has the same attacks, but it's bullet does not corrupt the environment anymore. Corruption is still a bit more complicated to contain than Crimson, because the vines can spread across a dug out trench.