Should I leave hyphenation on?
Leave it on. Hyphenation has a bad reputation from word processors, where it splits words at careless places. In a book it is doing something specific and necessary.
Why a book needs it
Justified text has to reach both margins on every line. The only elastic in a line of type is the word spaces, so when a long word won't fit, every gap on that line stretches to cover for it.
A book measure is narrow — around 60 to 70 characters. There are only ten or twelve gaps on a line to absorb the slack, so one long word turned away can visibly blow a line apart. Hyphenation gives the line somewhere to put the difference.
Turn hyphenation off and you don't get a tidier page; you get a page with wider and more uneven word spacing, which is the thing readers actually notice. If you dislike hyphens enough to switch them off, switch the text to ragged right at the same time — unjustified text has no gaps to stretch, so it doesn't need them.
Where the breaks come from
Words are split at proper syllable boundaries using a real US English hyphenation dictionary, not by guessing at the middle of the word. That's the difference between pro-fessional and profes-sional.
Names and capitalized words
There's a second switch: Hyphenate names and capitalized words, off by default. Breaking a character's name across a line looks worse than breaking an ordinary word, and invented names in fantasy and science fiction are exactly the words a dictionary is least able to split sensibly. Leaving this off keeps proper nouns whole.
Hyphen ladders
Three or more hyphens stacked down the right edge form a ladder, and it's distracting even to a reader who couldn't name it. Hyphen-ladder repair is on by default and re-breaks those paragraphs so the run is cleared.
The export report tells you the longest ladder left in the book and what proportion of your lines end in a hyphen — under about 10% is normal for a novel. See What is in the export report?
The ebook is separate
Ebooks reflow, so hyphenation there is a different question with its own setting. See Ebook settings.