Wishes made to a person right in front of you generally start with "que" plus a verb in the subjunctive present. There are several other cases of sentences starting with "que", such as when you're insisting with a "yes" or "no" answer (see the example below).
If you're interested about the grammar involved, this "que" is considered a "particle" by the Spanish Academies and not a subordinator, although I'm sure there's syntacticians who would talk about underlying verbs here (such as an underlying deseo (que)
'I wish (that)', espero (que)
'I hope that' or insisto en (que)
'I insist that').
Some examples of second-person wishes made this way:
Que sueñes con los angelitos.
'Dream about angels.'
Que salgas bien en los exámenes.
'I hope you do well in the exams.'
Gracias, que tengan un buen día.
'Thanks, (I hope you) have a nice day.'
Que sean muy felices (en su matrimonio).
'I hope you two will have a happy marriage.'
And just out of interest, some other uses of sentence-initial que:
—Sí lo hizo. —No, no lo hizo. —Que sí. —¡Que no! —¡Que si lo hizo! —¡Que no!
"He did do it." "No, he didn't." "Yes he did." "No he didn't!" "He did!" "He didn't!"
(Insistence in "yes"/"no" answers.)
Que los niños sean niños.
'Let the children be children.'
(Durante una oración.) Que mejore mi amigo Félix de salud, que Heriberto se acuerde de nosotros...
(During a prayer.) 'I'm praying to you that my friend Felix improves in his health, that Heriberto remembers us...
(Same as above.)
Que salga de ahí ya—ya tenemos que irnos.
'I want her to get out of there right now —we have to go.'
(Third-person "imperatives" or orders.)
Que me traiga un sándwich, ¡es una orden!
'I want him to bring me a sandwich, it's an order!
(Same as above.)
¿Que no nos traen los libros a tiempo? Hacemos una queja formal. ¿Que sí los traen a tiempo? Todo está bien.
'What if they don't bring the books on time? (Well, in that case) We do a formal complaint. What if they do? Everything's ok.'
("Conditions" or suppositions. All four sentences in this example are said by the same person, who's just throwing conditions at the listener without being asked.)
(Preceded by a:)
A que el mago viene tarde.
'I bet the magician's gonna be late.'
A que te metes en un lío serio si sigues haciendo estas cosas.
'You keep on doing these things and (I bet, I can assure you that) you'll get in deep trouble.'