There are different views on the true essence of teyyul-ard. One would be the theory of “اعدام و ایجاد” or “Existentiation and Elimination” of the renowned mystic, Ibn Arabi. According to this theory, the person eliminates his existence in one place and existentiates it in another. Another theory says that it is the teleportation of the body which takes place in individuals with very strong souls.
In any event, no matter which of the two theories we take on, it must be said that this is something that doesn’t take place for many people and only those who have high spiritual ranks and are friends of Allah (swt) ever achieve such a thing.
Regarding what teyyul-ard truly is, and to present an explanation for the concept and an intellectual analysis of it, there have been efforts made by different scholars. One of the theories for it is the theory of “اعدام و ایجاد” or “Existentiation and Elimination” presented by Ibn Arabi and accepted by some great scholars. According to it, the person practicing teyyul-ard eliminates his existence in one point and existentiates it in another.
This theory is based on the “Substantial Motion” of philosophy, or the “Renewal of Essences” of mysticism. According to the “Renewal of Essences”, everything, and according to “Substantial Motion”, only material things, in contrast to their apparent stability, are continuously becoming non-existent in an instant and existent in the next through grace. In other words, things are continuously receiving grace from Allah (swt) thus remaining and existing, such that if He was to deny them His grace, they would all remain in a state of non-existence.
Take the light bulb for example; it seems to be continuously on, but is not. Every second, it is receiving new energy, and if for one second, it doesn’t receive it, it will remain off. To put it in better terms, the light bulb has a nature of being dark and off all the time, but as it receives energy, it turns on and continues to remain on, so it seems. But in reality it is turning on and off so fast that the naked eye conceives it to be continuously on, as does the mind.
The same applies to things in this world, in every second they become non-existent and in the next, they are granted new existence, but since this happens so rapidly, we don’t feel it and think that everything is stable and ongoing.
Now, one who possesses the power to do teyyul-ard, actually separates his point of non-existence from the point of existence and transports himself from one point to another without any laws of time and place being broken, and without anything in relation to other things changing at all. Even if such a person didn’t practice teyyul-ard at all, he would still be undergoing “elimination and existentiation”, now that he is practicing it, he is also undergoing the same thing, the only difference being that the point and place in which each of these is taking place for him is different. Before, he would regain existence at the same spot, now he regains it elsewhere.
This is Muhyiddin’s theory and explanation of teyyul-ard in a nutshell.
According to the other theory we mentioned above, teyyul-ard means for a person enjoying a high rank of spirituality through asceticism and self purification and struggle, gains a strong soul in which is in total control of the body. As rapidly traveling is something that the soul is easily capable of, it becomes the same for the body as well.
The teyyul-ard that takes place for the elite and chosen ones is the result of self purification and religious asceticism by which the body takes on the attributes of the soul, enabling it to be like the soul in strength.
 Kashefi, Muhammad Reza, Porsekha va Pasokhaye Daneshjouyi, pg. 11; Erfan va Tasavvof, pp. 144-145.