Clary's fifteen years old. While that doesn't automatically make this a young-adult book, it's filled with a lot of young-adult themes: dating, identity, a changing view of the world. Plus, Clary has to complete her quest without any help from adults. In fact, many times adults end up being the bad guys Clary has to battle.
What was that about a quest? You've heard of the quest for the Holy Grail, right? This is similar, but it's more of a quest for the un-Holy Grail. Clary is initially searching for her mother, a quest that takes her all around New York City, above it, and below it. When she joins forces with Jace, her quest becomes two-fold. She has to rescue mom and recover the Mortal Cup—an artifact that makes people into Shadowhunters—before Valentine gets his grubby little hands on it.
See, Valentine wants to use it for evil, to build an army. Not good. This adds quite a sense of urgency, as Clary has to cavort around New York, into dark hotels that double as vampire lairs and decaying mental institutions that hide the villain's stronghold.