The various 10 incarnations of lord Vishnu are:
1) Matsya Avatar : in which he incarnated himself as a fish to get back the VEDA book from the 2 powerful demons, Madhu and Katan. Later he handed the VEDA to Lord Brahma and after killing of 2 demons, he created UNIVERSE from their powerful bodies.
2) Kurma Avatar : Lord Vishnu helped the people to win over all the Asuras , by churning the ocean, with the help of Madranchal mountain.
3) Apoorva Avatar : Through the Avatar of a Beautiful Lady, Lord Vishnu helped to form Amrut, the liquid of immortality, by hypnotizing the Asuras.
4) VARAHA AVATAR : King Kashyap???s son, Hiranyaksha, angry of staying in Pataallok and jealous of the people on Earth, worshipping Lord Vishnu, takes back the Earth to PATAAL LOK, i.e OCEAN. Seeing this, Lord Vishnu incarnates himself as a WILD BOAR, WARAHA and fights with Hiranyaksha and kills him and saves the Mother Earth and gets back the Mother Earth in the Universe.
5) NARSIMHA AVATAR : Being angry that his brother was killed, Hiranyakashyapua gets all powers granted to him by Lord Brahma. But misuses them to harass people on Earth. Prahlad, a great devotee of Lord Vishnu also was harassed. So Lord Vishnu incarnates himself as Narsimha ---Half Human body and Half Lion form to kill Asura and protects his devotee Prahlad.
6) VAMAN AVATAR : To protect God Mother, Aditi, Lord Vishnu became Vaman, Brahman Pandit, having all powers of Brahmaji and defeated all the Asuras. Lord Vishnu hands over PATAAL LOK to the Asura and takes the Entire Universe from Asura Bali.
7) Parshuram Avatar : To save the Society from the wickedness of the cruel King Arjun, Lord Vishnu incarnates as King Parshuram and kills him.
8) Shree Ram Avatar : Ravan , son of Sage Rishab, was blessed by boon from Brahma that he can neither be defeated by man or any Demon. So Lord Vishnu incarnates as Shree Ram, kills Ravan, who kidnaps his wife, SITA, thus bringing an end to cruelty, wickedness, violence...