Learn Turkish: Ölüm, hayatın doğal bir parçası.

In Turkish, a comma is often used to clearly mark the subject of a sentence. It separates the subject from the rest of the phrase, which is especially helpful in 'to be' statements like this one that don't end with a standard action verb.

How does the grammar of hayatın doğal bir parçası work?

This is a genitive-possessive noun phrase (often called a noun compound), interrupted by modifiers. Hayatın (of life) takes the genitive suffix -ın, and parçası (its part) takes the possessive suffix -sı. The descriptive words doğal bir (a natural) simply slip directly between the two linked nouns.

Why is the word order doğal bir parçası instead of bir doğal parçası?

In English, we say 'a natural part,' putting the article first. In Turkish, the indefinite article bir almost always goes directly before the noun and after any adjectives. It essentially reads as 'natural a part.'

Where is the verb? Shouldn't it end in parçasıdır?

This is a nominal (verb-less) sentence that creates an 'is' relationship. While you could add the copula suffix -dır / -tır to make it parçasıdır (which makes it sound like an objective, encyclopedic fact), Turkish very often drops this suffix in everyday statements. The 'is' is perfectly understood without it.