The quintessential English sentence has the familiar syntax Subject-predicate: thus, John hit the ball is a meaningful sentence because it corresponds to this familiar structure.
The parts of speech (POS) are broadly classified into eight categories, and each speech part has been ascribed its characteristic function: thus, while nouns name things, adjectives qualify nouns, and adverbs in turn qualify adjectives (along with verbs and adverbs themselves.)
It's under this classification scheme that we make sentences in English. Parts of speech, although they are mere labels which don't mean much per se, allow us to turn otherwise meaningless word bunches into proper sentences. Imagine them as slots into which must go the right words if we are to make such proper sentences.
It is for this reason that My plants are good for me is a meaningfully sentence. You are adhering to the established syntax and putting the right words into the right slots. The determiner my is precisely in the slot where it should be (it should be modifying the noun coming next to it and that's what it's doing), the familiar S-V structure is obeyed (although that's not compulsory every time), and so forth.
Likewise, My plants and pets are good for me reads like a fine English sentence because again the right words are in the right slots. The conjunction and is doing what it should be doing (it's piecing together word bunches), again the S-V structure is adhered to, and so forth.
Coming to the sentence Plants I don't nurture my, the reader stops dead in his tracks reading this. Why? Because the trained eye doesn't recognize the familiar syntax it's used to: something is amiss with this structure. On closer inspection one notices that the determiner my isn't doing what it should be doing. It has been shoehorned into the wrong slot. After all, it was meant to modify the noun plants. Of course, poets sometimes take poetic license and take liberties with syntax, but that is a different story.
So, the bottom line is that syntax is a useful tool that helps us to make sense of amorphous word bunches and communicate effectively with others.