This incarnation was demi-human- Half human and Half animal(lion). Nara means human simham means lion.
There is an interesting story to explain how and why God took this incarnation.
Once sage Doorwasa went to vishnu-lokha to worship Lord Vishnu. But the guards at the gate - Jayan and Vijayan didn't allow the saint inside to see the lord. The sage got very angry and cast a curse that the two should leave the heavens and be born in the earth as rakshasa- cruel and violent human beings and went away.
The two guards were very sad and worried. After thinking for a long time they went inside and saw Lord Vishnu. They told him about the curse cast by the sage Doorvasa. However even Lord Vishnu could not reverse the curse. The guards should not have stopped sage Doorvasa at the gate. Vishnu said You both should not have stoped that sage and I can do nothing about the sage's curse but I can give a new boon that is: you both can come back to me as my enemy after 3 births or you can come back to me as my devotee after 30 births. Take your choice. They said 'O lord we don't want 30 births. Please we want to come back to you soon in 3 births even though the three births would be as your enemies'. Lord Vishnu agreed to this. So in that order their first birth was as Hiranyaksha and Hiranyakasibu brothers. These brothers were very cruel. Hiranyakasibu was the worst of the two.
Once he rolled the earth like a mat and went with it under the sea. God got angry and incarnated as a boar. He dived into the sea killed the devil and raised the world above the sea on his snoot.
After his brothers death Hiranyaksibu became afraid for his life. He wanted long life and power. One day he got the idea to go to the forest and do penance to get more life and also ward off any trouble with any animal or the Gods. So Hiranyaksha went to the forest to do penance. After a severe and devoted penance for a long time God appeared before him. He asked God for immortality. But God said no. He said all men when born have to die some tim e or the other and cannot live for ever. God said "ask something else" Then Hiranyakasibu asked that he should not die either at the hands of any human or killed by any animal - in the day or at night. God gave him the boon asked for and disappeared.

Even though his wife was pregnant Hiranya-kasibu went to the forest to do penance.
In the meantime Indra thought "If Hiranyakasibu gets the boon that he wants then we will all be in deep trouble. Hence I should kidnap his wife and keep her in jail". So when he returned after kidnaping Hiranyakasibu's wife Naradha the sage came and stoped him. Naradha told Indra "you should not do this kind of coward acts. Hiranya-kasibu is definitely going to get the boon and nobody can stop him. leave the lady with me and go to your 'lokha'. Indra left that lady with Sage Naradha and went off. Naradha took that lady to his abode and told her good moral stories.She would listen to him but sleep off. At that time the Sage would start to tell the stories of God Vishnu and also Prayers to God Narayana. The child in the womb of the lady listened to all the stories about Narayana and also the prayers. These got embedded firmly in the mind of the child-to-be born. The child when born was named Prahalada and he grew up as an ardent devotee of Lord narayana.
Hiranya-kasibu had ordered all his subjects and all around him to pray to himself and not to any god.Hence was much annoyed by the devotion of his son to lord Narayana whom to God Narayana whom he considered as his enemy.
Prahalada was ill-treated and tortured to forget god Narayana but could not get him to forget the Lord. Rakshasa Hiranya- kasibu lost all his patience and one day in irritation asked prahalatha "Ok my boy where is that god Narayana ? Can you show me"? "yes" said Prahalada.He is everywhere and anywhere. The Rakshasa asked his son " pointing to a pillar "is he in this pillar ?" "yes he is in this pillar" said the son. Immediately the rakshasa took his huge club and hit the pillar. The pillar broke in to two pieces and from it appeared Narasimha neither a human nor an animal ie (half man and half lion) and took the Rakshasa on his lap and killed him with his claws. Thus came to end the evil called Hiranya-kasibu. God took Narasimha avathar only to kill evil.

This was Lord's fifth incarnation to show people they should be devoted to the God.