Mystic powers are quite real as given in our Vedic scriptures.
What these yogic powers are and what they do is described in Srimad-Bhagavatam (11.15.3-8). There the Supreme Personality, Sri Krishna, says that master yogis have established eighteen types of mystic perfection, eight of which are primary, having their shelter in Him, and ten secondary, appearing from the material mode of goodness. The eight primary powers consist of anima, making one=s body very small; mahima, becoming very big; laghima, becoming as light as air; prapti, acquiring whatever one desires; prakamya-siddhi, experiencing any enjoyable thing; isita-siddhi, controlling aspects of material energy; vasita-siddhi, overcoming the modes of nature; and kamavasayita-siddhi, obtaining anything from anywhere.

The ten secondary mystic powers that arise from the material mode of goodness through yoga are freedom from hunger and thirst, the ability to see and hear things far away, to move with the speed of mind, to assume any form, to see the pastimes of the demigods, to attain whatever one is determined to do, to hold influence over others, to have power to know past and future, to be immune from heat and cold and other dualities, to know the thoughts of others, to be invincible, and to halt the influence of fire, sun, water, and poison.

Although these yogic powers may seem impressive, many of them have also been accomplished by the advancement of materialistic technology. For example, the Yoga Sutras of Patanjali states that by controlling the nerve-currents that govern the lungs and upper body, the yogi can walk on water or thorns and similar objects. To reach this perfection, the yogi may have to struggle and meditate for twenty or thirty years. Or a common man may go to the boatman and pay a small fare to immediately cross the river.

What is the advantage of practicing yoga for so many years simply to walk on water?  Similarly, from the anima-siddhi one can become so small he can enter into a stone or atom. But modern science has made tunnels through hills and mountains and have analyzed such small molecules as atoms, accomplishing similar results as the anima-siddhi. By scientific advancement we can also fly through the air, travel under water, or see and hear things from far away as on television or radio. Of course, there may be some things science cannot do, like the laghima-siddhi, which enables one to go to the sun planet by entering and then flowing into the rays of the sunshine. Or prapti-siddhi, which enables one to get anything by extending his hand and taking what he wants from anywhere. Although it may appear like he is magically producing the object, actually he is just taking it from someone else.

By the yogic power of isita-siddhi one can create or destroy an entire planet. This power is much stronger than the atomic bombs that can only blow up a small portion of this planet and never recreate it. The prakamya power allows one to perform wonderful acts within nature, while the kamavasayita power enables one to control nature. And there are many other forms of these mystic powers. Summarily, these mystic powers are attained by being absorbed during meditation in the qualities of the different elements that give one the ability to acquire the natural powers within them. A yogi then attains control over them, which manifests as mystic powers.  Through these mystic perfections one can derive many kinds of material happiness, but such power is still material. They are not spiritual.

Therefore, yogis who are absorbed in the use of these abilities or the happiness derived from such yogic powers cannot get free from the material creation. They may be able to perform so many wonderful miracles, but this is not the business of those who are actually spiritually advanced. Saints and sages who are pure in heart have no interest in displaying their mystical abilities, though they may have many. These yogic powers signify only a preliminary stage of spiritual advancement. Therefore, in Patanjali’s Yoga Sutras (3.51), it is advised that by giving up these powers the seed of evil is destroyed and liberation follows.

There is a similar statement in Srimad-Bhagavatam (3.27.30) in which Sri Krishna states that a perfect yogi no longer considers using mystic powers, which then makes the yogi’s progress towards Krishna unlimited and causes death to lose its influence over him. From these descriptions we can begin to understand that yogic powers, or other supernatural abilities one may possess by other means, such as from witchcraft, Tantraism, etc., may be useful in some ways, but if we are too focused on them they become little more than another snare of the illusory energy, maya, to keep one bound up in the material world. And using such mystical powers is another way of lording over and trying to control material nature for one=s own enjoyment. They can cause one to become proud and to lose sight of what we are meant to accomplish in this life. Patanjali describes in his Yoga Sutras (3.56) that perfection is attained only when the mind becomes as pure as the soul itself.

In Srimad-Bhagavatam (3.27.28-29), Lord Kapiladeva (an incarnation of Lord Krishna) explains that His devotee actually becomes self-realized by His causeless mercy, and, when freed from all misgivings, steadily progresses towards his destined spiritual abode and never returns to material existence. That is the ultimate perfection one can
achieve. In this way, we can realize that if one continues on the path of the real yoga process, regardless of whether one attains various mystical powers or not, he will still reach the perfectional platform in which everything else is automatically achieved. This is described in Srimad-Bhagavatam (11.15.33-34) by Lord Krishna where He tells Uddhava that those who are expert in devotional service claim that these mystic abilities are useless and impediments on the path of the topmost yoga, by which one attains all the perfections of life directly from Krishna, including mystic powers. Not by any other means but devotional service can one attain the actual goal of yoga.