Blatantly rewriting my answer to this question
The Anthill Would be More of an Ant Pile

As a living organism that needs to hunt, move and grow, remaining in one place would not be very good. The best solution is to act in a similar manner to army ants. Instead of always moving in a direction, they would move as a pile. The primary part of this pile would act as the anthill, with specialized ants guarding the outside. This caste would act as both the Immune system and skin, their best defense would be a combination of formic acid and trap jaws.
The Soldier Caste would also be present in the limbs (see further down) and in small numbers inside of the pile itself. They would be the most expendable of all castes and also the most common. The Soldier also takes on the task of telling the difference between friend and foe. Another caste similar to this would be the Drones, they would basically work as an extension of sight; while all of the ants would attribute to sight (giving Anthills 360 degree spherical vision), Drones would allow the Anthill to find food and predators much quicker.
Inside of this pile you would see a lot of odd grouping of different castes acting as different organs. The workers would act as the dirt on the diagram below.

The Queen; The Circulatory, Immune and Reproductive System
The Queen would serve three human purposes; The Spleen, The Bone Marrow and the Reproductive system.
- By laying eggs, she would be making members of castes, Doing this she works as the Spleen and the Bone Marrow. If the larva is a Drone, a Soldier or a Biter, then she made members of the Immune system acting as the bone marrow. If the larva is any other caste; Worker, Courier, etc then she has made members of the Circulatory system acting as the spleen. If she produces a queen, then the new queen will slowly bud off forming a new anthill, acting as the reproductive system (see the Reproduction System).
The Farms, Digestion
Ants as a species have been farming for over 50 million years. It is completely possible that a part of the digestive system would be a Farmer caste. Using aphid droppings or a kind of Fungus as food. This farming would have be the equivalent to fat storage in humans; the food produced would be used in case of lack of outside food. An interesting idea here is for ants to cultivate bioluminescent fungi in order to make themselves glow. The stomach as a digestive organ would not exist. It would be more akin to fat, since each ants would digest on its own, the stomach would only store food until an ant gets hungry.
The Reproductive System
Anthills would be a hermaphrodite species, able to act as both Male and Female. The female half produces Queens when resources are plenty and they have a mate to keep it alive. The male half provides the Queen with a place to grow while it is weak.
When the Queen produces a Queen (due to a high amount of resources available to the larva) The new Queen (or Princess) will fly into the Anthills mate where it will act similar to marsupial mammals. When inside the 'Father', it will be protected and provided with a breeding male to create a combination of genetic material. The new Queen starts to make its own ants, a specialized caste is needed (The Soldier Caste, see below) to tell that the Princess is not an intruder and alert other ants of this difference. As the Princess' ants grow in amount, she will start to bud off and eventually become her own Queen of a new Anthill.
Soldiers, The Immune System

As said above the Soldier Caste is the most important of all castes, they would be built to prevent disease from spreading by catching it and abandoning the pile, like a sick dog. Also the dumbest caste, they are weaker in all but 2 regards (in which they are ahead by a wide margin); Fighting and Smelling.
- They are are extremely powerful, using the 2 best weapons an individual ant has: Trap jaws and Formic acid. Trap Jaws, as seen above, work as razor sharp biological mousetraps delivering a very powerful bite. Formic acid is the simplest carboxylic acid, most commonly found in ant venom.
- Their defensive skills are matched only by their sense of smell. They can smell the difference between friendly things, such as other random anthills and enemies, such as predators or anthills with intent to harm and then transmit a scent to the rest of the colony with instructions to treat them as a friend or foe.
The Nervous System
Information and coordination works via pheromones and shared stomach contents between Ants, with no central controller, this is the primary difference between an animal and a collective. A specific caste, the Courier, specializing in sending messages directly to distant reaches rather than diffusing slowly through the population allows for the collective Anthill to think. These can relay messages from one organ to another, directly and quickly. Like an octopus, the Anthill has distributive intelligence, Couriers are found in every part of the pile. Couriers are not like nerve tissue, they are nerve tissue.
The Couriers work by using pheromones, which in turn rely on the hardest sense to duplicate; smell. These pheromones work much like electrical energy in the human brain, though not as efficient, they replace intelligence for a better rounded creature.
Growth and Death
The only factor that limits an Anthills growth is the amount of resources available to it. Similar to a cell, where at a certain size the food will not be able to reach the nucleus, size is a factor for Anthills. If the anthill becomes to large it will need to not only always eat, but be on a food source. Unlike most Earthern animals, age and size have no similarity or connection in Anthills. After a new Anthill buds off, it will technically be fully grown, though the will still age. An Anthill will likely be considered 'fully grown' when it is able to reproduce (though cultural reasons may change this)
When it comes to aging, wounds and disease, Anthills are practically immortal. The Queen simply replaces herself as the spleen when she nears death, Wounds are not a problem due to the Anthills lack of blood and disease only kills an individual ant. Of course these are generalizations and they do have exceptions. For example, the Anthill has a very high metabolism and thus is very susceptible to starvation, especially in a community. Aging also has its limits, as (unless you go with the self reproducing method) the Anthill needs a mate to prevent dying of old age within 30 years, also even assuming the Anthill can endless provide itself with a new queen memory would be fading quickly after 100+ years considering smell is its primary source of memory. Wounds are an Anthills strongest immunity, the only way to kill an Anthill with wounds is to 1; kill the queen or 2; kill all the ants. Saying an Anthill is immune to disease is a stretch, because if the disease is contagious and the first ant to catch it spreads it before leaving, then the Anthill is like any other animal with disease.
Feeding
Emerging from the Central pile are "limbs" (I use the term loosely, a better name would be Chains) consisting of primarily Soldiers with a few Couriers. these will protrude from the central pile for many different reasons.

To meet a predator early on, same reason you put an army outside the castle. By fighting the enemy from a distance, you decrease the odds of damage to the central pile.
Hunting. If it takes less energy to drag the prey to the central pile than to move the pile (which, unless it ways equal to or more than the pile it is) then it makes more sense to drag the prey.
- On of the biggest advantages to a collective over monobodied animals is their ability to spread out and search as a group. For example, if the Pile is starving they can send multiple chains in random directions, follow the one that finds food and let the others die.