I read from a mythological story that Fire (Agni Lingam) is entirely different and much more important than the other pancha bhoota: Water (Appu Lingam), Sky (Akasha Lingam), Air (Vayu Lingam), Land (Prithivi Lingam).
Is this true? If yes, why?
Because Fire is the Only Tattva, which doesn't get impure. Other tattva like Water, air etc can get impure. That's why it is used in cremation too.
Related question : Why do Hindus believe in cremation instead of burial?
There is a story in Mahabharata Santi Parva about a time when virtue and vice disappeared due to unrestrained sexual indulgence. Then the Vedas disappeared. When both the Vedas and righteousness were lost the gods were possessed by fear. Overcome with fear they sought the protection of Brahman. The gods said unto Brahman with joined hands, 'O god, the eternal Vedas have been afflicted in the world of men by covetousness and error. For this we have been struck with fear. Through the loss of the Vedas, O Supreme Lord, righteousness has been lost. For this, O Lord of the three worlds, we are about to descend to the level of human beings. Men used to pour libations upwards while we used to pour rain downwards....." (REF: the 19th century translation of the Mahabharata by Ganguli, Santi Parva, Section 59], Ganguli remarks that men by pouring libations of clarified butter on sacrificial fires, feed the gods. The latter fed by these libations, pour rain on the earth whence men derive their sustenance. Men therefore are said to pour upwards and the gods pour downwards.
It must be remembered that in the old Vedic sacrificial dharma the only link between the Vedic gods and men was the sacrificial fire. Thus fire has a special place in the Vedic dharma.
Ankit Sharma's answer is absolutely correct. Five elements can cleanse a person's body of its impurities. Water washes, air removes the carbon dioxide from our body, earth decomposes our body, or almost anything (eventually in time at-last), and I don't have a clear idea how sky actually does it. But Agni being the superior because Agni can clean any impurity completely and without contaminating itself. Which is why Hindus burn/ cremate a dead body. Anything touched by Agni attains complete purity. It is also believed that Agni can not harm anything that is 100% pure, which is the reason why Sita devi was unharmed after the Agni-Pariksha.