Meaning of Hari (हरि)
This word हरि – is derived from Sanskrit dhatu हृ meaning “to take, carry, strip off”
हरति पापानीति हरि: ( the one who take away or remove sins)
In the fourth Manvantara when Tamasa Manu (तामस मनु) was the Manu, during that Manvantara Supreme God took incarnation as “Hari”, and he saved the Gajendra (गजेन्द्र) from the crocodile.
The same story is called as Gajendra Moksha (गजेन्द्र मोक्ष)
Reference in Shrimad Bhagavata Purana:
It is mentioned in Srimad Bhagavata Purana 8.1.30
तत्रापि जज्ञे भगवान्हरिण्यां हरिमेधस: ।
हरिरित्याहृतो येन गजेन्द्रो मोचितो ग्रहात् ॥
Also in this Manvantara, the Supreme Lord, Vishnu took birth from the womb of Harini, the wife of Harimedha, and He was known as Hari. Hari saved his devotee Gajendra, the King of the elephants, from the mouth of a crocodile.
Reference in Vishnu Sahasranamam:
As mentioned by Adi Sankaracharya in the commentary of Vishnu Sahasranamam verse 82
सहेतुकं संसारं हरतीति – Since Lord take away the world with its cause (ignorance), so called as Hari (हरि)