Learn Farsi: دلیل کشته شدن حیوان‌ها توسط شکارچی، شکار غیرقانونی است. - The reason for the animals being killed by the hunter is illegal hunting.

This is a passive infinitive acting as a noun. It is formed by taking the past participle of a verb—in this case کشته (killed)—and adding the infinitive شدن (to become / to be). Because infinitives in Farsi can be used just like nouns, کشته شدن literally means "the being killed" and acts as the object of the "reason" in this sentence.

Why is there an "e" sound (Ezafe) connecting شدن to حیوان‌ها?

Since کشته شدن is acting as a noun phrase in this sentence, it uses an Ezafe to link itself to the animals. Just like you would say کتابِ من (my book), here you say کشته شدنِ حیوان‌ها to mean "the being killed of the animals". This is actually part of a longer Ezafe chain starting at the beginning: دلیلِ کشته شدنِ حیوان‌ها (the reason of the being killed of the animals).

What is the role of توسط in this sentence?

توسط (tavasot-e) means "by" or "by means of". In Farsi, when you use a passive verb (like being killed) but still want to mention the person or thing that actually did the action, you introduce them with توسط. Here, توسط شکارچی tells us the animals were killed "by the hunter".

How does the word غیرقانونی break down to mean "illegal"?

The word قانونی (ghānuni) means "legal" or "lawful". The word غیر (gheyr) is an Arabic loanword meaning "non-" or "other than". It uses an Ezafe to attach to an adjective to create its opposite, so (often typed as a single word or with a half-space: ) literally means "non-legal" or "illegal".