What is the meaning of 省 in character breakdown
「省」 means graphically reduced, i.e. not the entire structure of the component is incorporated.
The given definition largely comes from Shuōwén jiězì:

《說文》：“喬，高而曲也。从夭，从高省。《詩》曰：‘南有喬木。’”

and since Shuōwén jiězì descriptions are linked to Shuōwén small seal script shapes, by looking at these shapes the description would make more sense.
　　　　　　
Basically, Shuōwén thinks that 「喬」 is 「夭」 on top of 「高」 with its top 「亠」 removed, hence its description of the 「高」 part as graphically reduced (省).


To my understanding, when a character is of the 会意 type, part of the character might be both phonetic and symbolic.

No, 「會意」 means compound semantic, that is, all components hint at meaning. If something is simultaneously a semantic and phonetic component, the literature normally says something like 「从Ｘ从Ｙ、Ｙ亦聲」, e.g.

《說文》：“墨，書墨也。从土，从黑，黑亦聲。”


By the way, that description

《說文》：“喬，高而曲也。从夭，从高省。《詩》曰：‘南有喬木。’”

is incorrect, 「夭」 does not give a meaning hint in 「喬」, and is the result of graphical corruption.