What it means
ように
at the end of a sentence is a set expression for the volitional subjunctive. In layman terms, it means the preceding sentence is a wish!
Why it means that
様{よう}
is "a word that expresses the state of things". に
is a target particle. Therefore, if it helps you understand, ように
means "towards a certain state". So when I say something like
明日{あした}は晴{は}れるように — May it be sunny tomorrow
I'm saying "towards the state of things where it's sunny". As happens frequently in Japanese, I am omitting the verb of this sentence because it is obvious in context.
明日{あした}は晴{は}れるように祈{いの}ります — I pray it may be sunny tomorrow
It expresses a yearning for a particular 様{よう}
.