Krishn was the 8th Avataar of Vishnu in Dwaapar Yug on this Prithvi. He came here as Poorn Avataar, means that He came here with His all powers. Powers means with 16 Kalaa (10 Indriyaan, 1 Man, and 5 Bhoot (Prakriti - Jal, Vaayu, Prithvi, Aakaash, and Agni). Others had fewer Kalaa. He is called Yogee Shree Krishn.

He was born in Vasudev-Devakee's house, in prison, in Mathuraa, but was brought up by Nand and Yashodaa up to 11 years of age in Gokul.

While He was in Gokul, or precisely in Nand Gaanv, He killed several Raakshas - Pootanaa, Bakaasur, Aghaasur etc as and when Kans sent them to kill Him and did several activities which were not possible for a human child of that age. All these are said to be His Baal Leelaa. Later He killed Kans, Shishupaal, Dantvakra, Kaalyavan, Paundrak, Bhaumaasur, Shaalv, etc. During His life time He freed some divine souls also who were living here on Prithvi as Shaap, such as Yamalaarjun in the form of trees, Raajaa Nrig in the form of chameleon. He fought with Jaraasandh 17 times, but He did not kill him. Then He inhabited Dwaarakaa Nagaree (built by Vishwakarmaa) in the sea and took His people there.

He had 16,108 wives. All lived in their own palaces and Krishn used to live with every wife separately in harmony. Among them 8 were His Pat-Raanee (chief queens). Their names were: Rukminee, Satyabhaamaa, Jaambvatee, Kaalindee, Mitravindaa, Naagnjitee, Lakshmanaa, and Bhadraa. He produced 10 sons from each of His wives.

Paandav were His father's sister's children, Kuntee was His real  Buaa. He helped them in many ways during their life time. He helped them to regain their kingdom too. Arjun and Draupadee were specially dear to Him. Arjun and Krishn were the Avataar of Nar Naaraayan. He delivered the knowledge of Karm to Arjun in battlefield which is popularly known as Bhagvad Geetaa (song of Bhagavaan). Later when he had finished His work here on Prithvi, He delivered the knowledge of Bhaagvat to Uddhav Jee before going to His Lok. He even killed His own Vansh through  Brahman's Shaap.

The whole 10th Skandh of Bhaagvat Puraan is devoted to Him.

He has several names:
Achyut
Baankeybihaaree
Banseedhar - who bears flute
Giridhaaree - it was when He lifted Govardhan Parvat on His little finger
Gopaal - who rears cows
Govardhandharee - same as Giridhaaree
Kanhaiyaa
Krishn - who is of dark complexion
Maadhav
Mukund
Muralee Manohar - who has heart-stolen flute
Muraleedhar - who bears flute
Nand Nandan - son of Nand Jee
Nandlaal - son of Nand Jee
Shyaam - dark complexioned
Vansheedhar - who bears flute
Yashodaa Nandan - son of Yashodaa
etc etc