Answer: By writing that "No man is an island, entire of itself...", the author means that humans aren't meant to be isolated (like an island itself), an that they depend on social relations for survival and social purposes.
Explanation: It's easy to see that the author criticizes the concept of isolation, because on the next lines of the same poem, he says "Every man is a piece of a continent, a part of the main", which, again, states that every man depend on each other and must mingle in order to be empathetic.