He was the son of sage Jamadagni and Renuka.Rishi Jamadagni was known for his temper.
Parshuram was a devotee of Shiva and he received a Parshu (a weapon) from Lord Shiva as a boon thus the name Parshram was given to him. Shiva also tought him war skills. As a child Parshuram was a keen learner and he always obeyed his Father Rishi Jamadgani. Parshurama was the first Warrior Brahmin and he is also called Brahmakshatriya (both Brahmin and Kshatriya means warrior) his mother Renuka Devi was a daughter of Kshatriya’s .And after receiving a Parshu from Lord Shiva it has become impossible for any one on the earth to defeat him.
Parshurama’s parents were great spiritual achievers his Mother Renuka devi had command over the water elments and his father Jamadgani over fire. its even said that Renuka devi could fetch water in the even in a wet clay pot. Once Rishi Jamadgani asked Renuka Devi to fetch water in the clay pot, some how Renuka Devi was distracted from the thought of being a women and the clay pot broke. Seeing Renuka Devi wet the enraged Jamadgani called his son Parshurama. He ordered Parshurama to cut Renuka devi’s head. Parshuram obeyed his father. Rishi Jamadgani was so pleased with his son that he asked him for a boon. Parshurama asked Rishi Jamadgani to restore the breaths of his mother, thus Rishi Jamadgani who was the owner of Divya Shakties (divine Powers) brought back the life of Renuka Devi.
Rishi Jamadgani and Renuka Devi both were blessed not only for having Parshuram as their son but they were also given the Kamdhenu Cow. Once Rishi Jamadgani went out from his Ashram and in the mean while some Kshatriyas (worriers) arrived at their Ashram. They were in search of food, the Ashram Devies gave them food they were so surprised to see the magical cow Kaamdhenu, the cow would give any Dish she asked for. They were so amused and they put up the purposal of buying the cow for their king Kartavirya Sahasrarjuna, but all the Ashram sahadus (sages) and Devies refused. they forcefuly took away the cow. Parshurama killed the entire army of King Kartavirya Sahasrarjun and restored the magical cow. In Revenge Kartavirya Sahasrarjun’s son killed Jamadgani. When ParshuRama returned to the ashram he saw his father’s body . He noticed the 21 scars on Jamadgani’s body and took the pledge to kill all unjust kshatriyas 21 time on this earth. he killed all the sons of king.
Parshurama tought war skills to Bhishma Pitamha, Dronacharya and even to Karana. (all these are characters of Mahabharata). Parshurama is Immortal it is even belived that he still lives on the earth and he will even teach war skills to Kalaki, the tenth Avatar of Vishnu who is come on the earth in the end of Kalyug.
Once Parshurama went to see Lord Shiva on Kailasha . Lord Ganesha came into his way, who was ordered by his mother Parvati to prevent anybody to come and disturb them. Parshurama threatned ganesha and ask him to fight with him if he want to stop him from meeting Shiva. In this fight Parshurama cutt off Ganesha left Tusk. when Goddess Parvati saw this she lost her temper. godess took the form of Adhhi Shakti in anger that even shiva was unable to please him. She told that Parshurama is not satisfied with the blood of Kastriya’s that he wants to harm my son. Ganesha asked his Mother to forgive Parshurama and he some how succeded in pleasing his mother. Parshurama was so pleased with Ganesha that he gave him his parshu and blessed him.