Learn French: Je comprends ton envie de rentrer. - I understand your desire to go home.

Even though envie expresses a desire, the subjunctive is only triggered when you have two different clauses connected by que (for example, Je veux que tu rentres). Here, the desire is expressed as a simple noun (envie) followed by the preposition de and the infinitive verb rentrer.

Envie is a feminine noun. Why do we use the masculine ton instead of ta?

You are right that it is une envie. However, because envie starts with a vowel, French uses the masculine possessive adjective ton to make pronunciation smoother. Saying ta envie would create an awkward clash between the two vowel sounds.

I usually see envie in the expression avoir envie de (to want). Can it be used on its own like this?

Yes! While the verb phrase avoir envie de is extremely common, envie is simply a noun meaning a "desire," "urge," or "craving." In this sentence, ton envie translates directly to "your desire."

Why does rentrer mean "to go home" here? Doesn't it mean "to re-enter"?

While rentrer literally means "to re-enter" or "to go back in," it is the most natural and common way in everyday French to say "to go home." You don't usually need to add chez toi or à la maison for the meaning to be perfectly clear.