The first avatar, Matsya represents alertness and vigilant awareness. When Lord Brahma was asked to read the Vedas to gain the knowledge to create, he dozed off, after a while. The demon Somakasura then stole the Vedas. Lord Vishnu incarnated as a fish to retrieve the Vedas from the demon.
Lord Brahma is symbolic of a student who is distracted from his studies and loses excellence in studies to the demons of laziness, fatigue and temptations.
Next, when the Devas and the Asuras churned the ocean of milk to extract Amritam (nectar), Lord Vishnu incarnated as Kurma Avatar (Tortoise). The churning of the ocean represents industry and activity involving tapping of natural resources and the combined effort of all members of an organization. The sinking of the Meru mountain represents failing confidence.
The tortoise here represents self-confidence. It is only with immense self-confidence that one can achieve one’s goals and also the nectar of immortality.
Third, the Lord incarnated as Varaha (Boar) to kill the demon Hiranyaksha who had stolen the Earth itself for his personal greed. Hiranyaksha, meaning the one with eyes made of gold, symbolically represents materialism that seeks to conquer and subdue the whole Earth for personal greed and wealth.
Varaha Avatar represents the transformation of materialistic desires into spiritual desires. Varaha means the day of auspiciousness which represents a positive turning point that comes in the life of every individual which helps him or her to outgrow materialism and yearn for spiritual awakening.
Fourth, the Lord incarnated as Narasimha (Half-Man, Half-Lion) to kill the demon Hiranyakashyapa, brother of Hiranyaksha.
Samskaras (cultural training) should be imparted to children even while they are in the womb. There are many instances in our scriptures like the story of Prahlada who learnt the Narayana mantra from Narada Maharshi and Abhimanyu who learnt the art of war (Chakravyuha) from Lord Krishna while still in the womb.
A demon like Hiranyakashyapa gave birth to a divine child like Prahlada because he uttered the name of Narayana three times. When Hiranyakashyapa retired to the forest to perform penance to seek boons from Lord Brahma, he heard a bird on the tree chanting the name of Narayana. Taking this as an ill omen, for he considered Lord Vishnu to be his enemy, he returned to the palace. When his wife enquired about the reason for his untimely return, he told her about the ill omen. Thus, even though he chanted the name of Narayana accidentally and reluctantly three times, this led to the conception of Prahlada who was born to become a great devotee of Lord Vishnu.
Hiranyakashyapa sought a boon from Lord Brahma with many difficult conditions that he should not be killed by man or god, with weapons, neither during day nor night, neither outside nor inside the house. Hiranyakashyapa thought he had fooled God and obtained a fool-proof boon of invincibility and he began to tyrannize and terrorize the worlds.
The Lord who is a symbol of Supreme Intelligence found a loophole in the boon and incarnated as half-man, half-lion and killed the demon during twilight at the entrance of his house on the doorstep.
The Lord here represents the Law which is meant for protecting Dharma and the good people of the world.