Vamana Avatar's ''three steps'' symbolize three human flaws that need to be controlled

Vishnu as Trivikrama, Mamallapuram, Tamil

Maha Vishnu is one of the Trinity Gods in the Hindu pantheon and he in in charge of protection of all living things, the other being God Shiva, taking care of destruction of humans, etc and God Brahma, in charge of creation of living things. Among them, Brahma has a few temples  dedicated to him and there are a few in Tamil Nadu and Rajasthan - this being due to a curse on him cast by God Shiva.

Trivikrama Panel Adivaraha Cave Temple)

Vamana Avatar. Vamanar putting the foot on Mahabali's head.

Vishnu covering the sky with his second stride.

Maha Vishnu is often referred to as ''Thiruvikraman'', meaning that he is enjoying happiness in all three worlds - earth, nether world and heaven. His name, in reality, has  philosophical connotations and is relevant to our lives. It implies all these three worlds are within us.  

Legend has it once Sri Vishnu took the  fifth avatar of Vamana (dwarf) in order to subdue the pride and presumption of King Mahabali who was otherwise a good king. As Mahabali was man of charitable disposition, Sri Vishnu in the guise of a Brahmin dwarf approached him and asked him to donate the land that could be covered by his three strides. Not realizing the little saint demanding so small a land was none other than Sri Vishnu, he agreed with scorn. Vamanar taking his Visvaroopam (giant form), covered the earth with one stride and the sky with his second stride. Vamanar asked Mahabali, ''Where can I place my third stride?''  Mahabali, who stood before the giant Vamana, was literally dumbfounded. He could not believe his eyes, Any way, unperturbed, the  king was particular  about keeping his promise.  so what he did was, with humility, he asked Vamana to put his foot on his head. Upon putting his foot on Mahabali's head, Vishnu said,  ''Regardless of your predicament, you have kept your promise and you will ever reside in the world of divinity''. This is the reason why Vishnu got the name Thiruvikraman. 

It is therefore wrong to conclude that Sri Vishnu pushed Mahabali into the nether world (pathal) by placing his foot on his head. 
The correct interpretation is by putting his foot on the king's head Sri Vishnu  blessed him, got rid of his  blemishes and made him part of his world so that he could lead a happy blissful life for ever.
God's avatars (incarnation) always have some hidden message for the humanity and it is for their betterment and welfare.  King Mahabali, though god-fearing and charitable, was overwhelmingly haughty and arrogant. So, the lord decided to correct him and make him understand his folly.

From the three strides made by Vamana, we can infer the 
following -------Vamana 's first stride covering the earth: It implies  that humans must stop being greedy and over ambitious.
etc. Must avoid bad habits and over involvement in sex.  They are all related to human body and its uncontrollable desires.

Vamana 's second stride: It implies that humans must get rid of rage, revulsion, fear, nervousness, etc; all related to  human emotions. To succeed in life and be happy we should not give room to them keep the emotions under control. 

Vamana 's third stride, placing the foot on the head of the king: It implies that all the bad and negative thoughts, including  king's ego,  arrognce, etc get buried for good and he  becomes a matured and  balanced man. No matter how great a man is, he must have humility.
As humans, we must learn to control all these temptations, emotions, etc, to lead a quiet and blissful life.  So,  the ''earth'' represents our body, the ''sky'' our breathing, emotions, etc and our ''inner feelings''- devotion, conscience, etc., represent the world of divinity. The three worlds that are within us are  Bhoologm (earth), Akasam(sky) and Deiveegalogam (conscience and devotion to god).

Dwarf Vamana avatar at Rani ki vav, Patan,

The other explanation of Vamana Avatar is Mahabali symbolizes Samridhi (prosperity), the three feet symbolizes the three states of existence  Jagrat ( consciousness, dreamless sleep; awake), Swapna (dream sleep; can nor perceive the external universe with senses) and Sushupti (deep sleep) and final step is on his head which elevates from these three states, unto moksha (spiritual liberation, release from rebirths, freedom from Samsara and  enlightenment)

Source: ''Aanmeegam Weekly Magazine'', Dinamalar 31 March, 2019