'In memory of someone' means that the thing described has been done or made to remind people of the person and to pay respect to them. 'In loving memory of' means the same thing but with the addition that the person was loved and will be remembered with love.

"Loving" is an adjective that modifies the noun "memory". As a noun, "memory" can be described by any adjective. You can have "a happy memory" "a bitter memory" "a loving memory". Present participles, like "loving", can *always* be used as adjectives. Here are some more examples showing participles being used in this way: "That was a fascinating movie" "He is a stimulating teacher" "That was a boring lecture" "English is a vexing language"

It means John's memory is loving