In the first sentence, the word human is being used as an adjective. What kind of survival? Human survival, meaning the survival of humans in general.
In the second sentence, human must be a noun, because it has the possessive 's, and only nouns and proper names can use that. But this causes a problem: human is a count noun, so you can't just say "human's survival", you need an article, like a human's survival, or this human's survival. Using human as a noun also changes the meaning of the sentence, because now you're not talking about the survival of humans as a general concept, but the survival of one particular human.
Another way you could phrase it is
It plays a crucial role in humans' survival.
This sentence uses humans as the plural noun, so it can still take the possessive, but it means "the survival of all humans". When you make the possessive of a plural noun that ends in s, you just add ', not 's.
Possessive-adjectives are not adjectives. Possessive pronouns are certainly not adjectives
Possessive-adjectives can function in some ways like adjectives (my book, red book). But they are can't form comparatives or superlatives (*a more my book, *the myest book). And they can't form a predicate (*this book is my.)
The possessive pronouns act like nouns. In modern English, they seem usually to appear in the predicate "It's mine!". In older forms of English they were seen in the subject (consider the Lord's Prayer: "For thine is the kingdom" thine is the old singular form of yours). Modern English seems to prefer "my one" in this position: "My one is better than yours."
Nouns and pronouns can appear as predicates. "It's a cat." "I want him." and so on. In the sentence "It's mine" the word mine is acting as a pronoun, not as an adjective. The word "mine" can't function as an adjective *"mine book" is incorrect.
It is best not to think of words like "my" as replacing adjectives. But instead, think of them as forming their own special class of words, which go before nouns to indicate possession.
Best Answer
I think you could say it either way, but you'd want to switch articles:
The latter uses "the human brain" in the general sense, as @MaulikV explains in his answer. The former talks about a person's brain in the indefinite sense.
I think the latter would be more appropriate for scientific contexts, yet the former is acceptable in casual conversation.
The format with the indefinite article also requires a possessive; consider:
Here, the indefinite article doesn't sound right. However, we can fix that with a possessive modifier: