So these people think that they can live with no food or water.
Indefinitely.

http://breatharian.info/

Here's the interesting part, their explanation(s):

(apparently they only hold true if you fit into a specific category, in which case three of their explanations are just false. Or there's a dual-dualism thing going on.)

HOW IS IT POSSIBLE ?

Explanations for the open-minded

"There are more things in heaven and earth, Horatio, Than are dreamt of in your philosophy." No matter whether we believe in something or not, the phenomenon takes place irrespective of our knowledge or belief. Besides, no matter how we try to explain it, is the explanation arrived at really so important? The most important thing is that from the beginning of our civilization, there always were people who never ate. Such people existed, exist and will exist, which means that we too have this capability. We only need to find a way to adapt the body to a different kind of energy processing.

Explanation for an esoteric person

Ubiquitous energy, whether called prana, qi, ki, orgon, liquid light or by other names, maintains the organism of someone who doesn't eat. A human body can be powered by prana if the subconscious (which manages the body metabolism and shapes the physical body) acquires the skill of automatic transformation of ubiquitous prana to satisfy the needs of a human body.

Explanation for a scientifically-minded

Of all the other organisms, the human body is the most complicated, integrated and self-regulated energetic system. It is complicated and in many aspects unexplored computer-mechanic-chemical formation, controlled by the brain with the whole layout of magnetic, electric and gravity radiation. This complicated machine can be adapted to all possible living conditions on Earth, if given enough time and developed in right way.
We haven't fully explored the human organism energy system. One of the ways of powering human body is energy and substances created by the chemical and physical factory of the body (excretory and respiratory system). Apart from this powering system, there is another, a reserve one (or maybe major one but moved away to the reserve role), which is able to transform the available energy directly. This powering system transforms the energy directly into matter, so in this way all that the organism needs. The pineal gland is claimed to have a crucial role in this process. This hypothesis is confirmed by research undergone on some  people, where CAT scanning shows a significant enlargement of this gland. The pineal gland manages (like a central processing unit) the mechanism of direct energy exchange between the organism cell and the surroundings (it actually occurs at a sub-atom level).
One explanation, purely scientific, which comes from a nuclear physic says as follows: the organism consists of tissues, which are built of chemical molecules, and next these molecules are built of atoms. Atoms consist of electrons and protons, which are built of smaller elements. As the result of this way of looking for an origin element, we reach the point, where the matter does not exist. There, we have only something, which we can call vibrational whirls of energy. As long as history exists it has been known under different definitions, for example prana, orgon, light. Hence such definitions originated such as "living on light" or "prana nourishment". All the matter which exists in the Universe, including the human body, is comprised of whirls of vibrational energy. The human body is the best well-known sophisticated, programmable and simultaneously self-controlled electronic-physical-chemical machine with a central management system, called the brain. There are centers in the brain, which manage body energy and chemistry (mainly pineal gland and pituitary). In this way, the organism lives and builds itself using these whirls of energy.

Explanation for a deeply religious person

God is everything. There is nothing which exists without God, there is nothing which has not been created by God. The inconceivable and almighty God is the only One and the highest perfection. Since the Almighty God has created everything and He/She/It is the highest inconceivable perfection, He/She/It can bestow the ability to live without eating on people of His/Her/Its choice.
Since God is inconceivable and almighty, it is no use asking how God is able to do this. Important is the fact that God can and does select people to receive this grace. We can ask God for the grace of not eating, because God listens to sincere requests of the devoted children.