Here, "each time" acts as a subordinating conjunction introducing the time expression, then, "it is given away" is a relative clause - specifically a defining relative clause because it provides essential information that defines when the goodness of life grows more magnificent.

Though it looks like a noun, the phrase "each time" is actually adverbial and modifies the verb "grows". It behaves similarly to the words "yesterday" or "Sundays" which can also be adverbs that look like nouns. Here are some similar sentences: "Her visits became more frequent Sundays" or "He played better music yesterday" or "The princess lived in a castle once upon a time".