  In a literal sense it means one who possesses a lot of calves, In relation to Vishnu - one who possesses lots of children, whom He protects like a cow protects its calves. Initial references of these interpretations are connected to the Krishna incarnation, where he protected cows and their calves during his childhood. The second interpretation refers to the innumerable hosts of souls who are to be always tended by Him, like a cow tends to its calves with affection.
It is observed by commenter on the Vishnu Shahstranama, that "Bhagvana's guna of being the Protector exhibits itself throughout life. Even before the child is born to a mother, He makes sure that the mother has the milk to feed to the child as soon as it is born, the mother bird and the child bird know how to transfer food through their beak etc. " VS construes that His Vatsalta (Divine Love) is not limited to the name. He says that He shall roam behind his devotees, take care of them, feed them and protect them from all sins. A scene plays in the mind, where during His Krishnaavatar, Lord Krishna saves his devotees (in the form of cows and calves) from Aghasur and takes them to the banks of Yamunaji. Leaving them to graze the green grass on the banks, Lord Krishna settles down with his other shepherd friends to eat lunch. He is putting a morsel of food in his mouth and suddenly hears the sound of a cow mooing loudly, for her calf is nowhere to be seen. Lord Krishna puts the food down and rushes to search for the calf, even though his friends insist that he eat and then all shall look for the calf. He assures his friends, Please eat and do not worry, I will go look for the calf and be back. He then proceeds to the mountains and caves to look for the calf. Such is His love for his devotees, for each being that is existing. The name Vatsi, shows the characteristic of being able to love as well as being loved. At each step of our lives we are face to face with various temptations which lure us away from our Lord.
Just like the shepherd runs here and there, in the fields, mountains and caves to look for his cows and calves, who have been enticed by the green grass and water, In the same manner, when we sprint towards materialistic matters and neglect Him for a matter of time, He comes in our wake to find us, to care for us and to protect us. Lord always saves and protects his devotees from the various traps and baits that cross our paths every second. Another meaning depicted for Vatsi is "the one who bears the symbol of a devotee". It is said that Brhighu Rishi had kicked Lord Vishnu in his chest.
Lord Vishnu not only forgave him for his peccadillo but also bore his mark on his chest. He demonstrates his love for his devotees by accepting their abuse and forgiving them for their worst sins. My heart that beats for Vishnu, seeks his forgiveness for following and indulging in various activities that stop me from being with him, chanting his name for every second.
I cannot say that I forget him ever, He is always there with me, to the extent of being along with me when I go to work, while I am going for demonstrations, while being stuck in some coding or otherwise. I understand here that He does not want me to leave living, He just wants me to live with quality, and under the guidance of His Divine Love.
Wherever it shall lead me, it shall lead only to a peace that I have never known before, an ocean of milkâ¦ where there is knowledge and light and most importantly oneness with my maker, my Vishnu, my soulâ¦ I do not question His presence, I know He is there, and even if I do somehow overlook Him, I am sure He will find a way back into my heart, my life and my soulâ¦ coz they are nor mineâ¦, the life, heart and soul all belongs to Him. I may think that I am a mere devotee, who is trying to search her soul for some tranquility, but I know, with His love for me is specail, and that makes me special.. I am special, someone specialâ¦ 
