To borrow a phrase from the old Star Trek series, the "prime directive" of the limbic brain is to ensure our survival as a species.
You have explained that it is the preposition "to" at the beginning of this sentence that is confusing you.
It is quite common to introduce a clause with a phrase containing to followed by an infinitive, for example:
To be honest, I don't really like Star Trek.
This means that the statement "I don't really like Star Trek" is you speaking honestly.
To borrow a phrase from the old Star Trek series...
This means that the clause which follows this statement contains a phrase from Star Trek, namely "the prime directive".
A commonly heard example of this is:
To quote Shakespeare... (before a Shakespeare quote!)
For information, in Star Trek, the explorers of space and alien worlds are governed by an overarching rule which they call "the prime directive". What that rule is in the context of the series is largely irrelevant here, but the point is that it is a comprehensive principle which governs all other rules and actions. The need to obey the "prime directive" is more important than following any other rule.
So, the writer is saying that our brain, which may have many different functions and "rules" that govern it, has a "prime directive", or overarching motive, namely survival.