The holidays are always a great opportunity to practice the que + subjunctive construction, which is one of the most common (and shortest) ways to express hope and good wishes in Spanish. This particular construction is very interesting because it involves the omission of the main verb, usually desear ("to wish"), but also querer ("to want"), esperar ("to hope for"), and others followed by the subjunctive. The result of doing this is a short phrase that is practical and meaningful. So, instead of saying deseo que te diviertas ("I wish you have fun") you can simply say ¡que te diviertas! ("[I wish] you have fun") which is more likely what a native speaker would use in a casual conversation.
Since this particular construction is used to express wishes or hopes to someone right on the spot, it makes use of the present tense and the present subjunctive. The main omitted verb desear ("to wish") is in the present tense: yo deseo ("I wish"). Therefore the action that you are wishing to happen must be expressed, after the conjunction que ("that"), in the present subjunctive: te alivies ("you get well"). The condensed resulting phrase is then: ¡Que te alivies! ("[I wish] you get well"), which we may as well just translate as "Get well!" Let's see more examples.
Mexicans use this construction a lot to wish you well while saying goodbye:
Hasta luego, nos vemos y... que se la pasen bien.
See you later, see you and... hope you guys have a good time.Play Caption
Argentinians also like to use it:
Chau, que le vaya bien, chau.
Bye, have a good day, bye.
Captions 38-39, Muñeca Brava - 9 Engaños - Part 4Play Caption
You can wish someone all sorts of good things using this construction, like to have a good night:
Bueno, yo también me retiro, que tengan muy buenas noches. -Buenas noches.
Well, I will also retire, good night to you all. -Good night.
Captions 98-99, Muñeca Brava - 43 La reunión - Part 2Play Caption
Or simply to enjoy something:
Eso es todo, gracias. Que disfruten de, del folklore de Puerto Rico.
That's all, thank you. Enjoy the, the folklore of Puerto Rico.
Captions 31-32, Baile Folklórico de Puerto Rico - Los BailarinesPlay Caption
Or to wish someone a nice Christmas:
¡Que tengas una feliz Navidad!
I wish you (have) a merry Christmas!