Que disfrutes de tus vacaciones
 

Hi,

In the English original the subject looks like Enjoy
your summer vacation.

Conjunction tables also look like this:

que (yo) disfrute
que (tú) disfrutes
que (él) disfrute

What does que mean in the subjunctive clauses? I suppose it's there just because it is; I'm in search of some means to wrap my head around it :) . How am I supposed to think about this que?

When the conjunction 'que' is used at the beginning of a clause (a clause contains a verb), the speaker is expressing a wish. The conjunction isn't translated into English, but it should be easy to detect that a wish or desire is the intended meaning. The verb is cast in the subjunctive mood, as you're already aware.
To wrap your head around that untranslated conjunction, it may prove helpful to learn that it does have an English counterpart-may. It may also be helpful to imagine that a conjugated form of 'esperar' may precede the conjunction, with almost no change in meaning-Espero que ('I hope you enjoy ...').

In English, "Enjoy your vacation," is always interpreted as a wish (never a command).
"I hope you enjoy your vacation," is another way to express the same thing, using obvious 'wish' language.
"May you enjoy your vacation," is not heard as much, but is another way to express a wish. This, I believe, would be the exact transliteration of 'Que disfrutes de tus vacaciones'.

In other sentences, like ¡Qué rico!, the leading word is not a conjunction (notice there's no clause, which always contains a verb). Here, 'qué' is an adverb, qualifying the adjective 'rico,' and its English translation is often the word 'how.' The vowel should have an accent mark.

Thanks! Priceless.