Plot/Story
Warning: I'll try not to put in any major spoilers, but for those of you who absolutely detest the slightest spoiler, stop reading here.
The story kicks off when Kensuke, a male high school student with a more developed sixth-sense than most, meets Kagura, an female exorcist. From then, the (rather good)plot rolls faster and faster. To be honest, though, while the plot is certainly good and the storyline deep and strong, it's not amazing. However, the emotions it brings out of you more than make up for it. I hate long plot summaries, so just go read it and see if you like it.
Characters
(first, last)
Kensuke Nimura - Male, one of two main protagonists. Age: high school freshman to sophomore. Parents are overseas. Trained in kendo. Has the ability to see spirits.

Kagura Tsuchimiya - Female, one of two main protagonists. Age: high school freshman to sophomore. Parents deceased at young age. Trained in various exorcist skills (has the ability to see spirits).

Yomi Isayama - Female, main antagonist. Age: Not specified; likely around 5 years older than Kagura and Kensuke. Parents deceased at young age. Deceased herself (yeah, complicated). Was an exorcist.

Others - There are probably around 10 other important characters, but I don't think it necessary to list them here.
Drawing Style
Just wow. The art is top-notch, on par with Vampire Knight and other shojos that stress the art more heavily despite being shounen. Incredible amounts of detail, backgrounds/scenery are beautiful, characters look amazing. Occasional chibi-esque cutesy faces are a plus (OwO, etc. If only I could find a way to display them via text). Contains an amount of blood/gore/gross monsters, but only enough to scare away strictly shojo readers. Just one small complaint: the battle scenes look great, of course, but don't flow perfectly. Most of them only take a few panels to display a good deal of movement, which in my opinion isn't good. BUT, it doesn't really take away from the reading and gives more pages of juicy plot. - Side note: does include some ecchi/fan service, but not too much.
Enjoyment
I absolutely LOVED this series. I flew through it (52 chapters) in one school week, and subsequently failed a few tests. <.< But it was worth it (or rather, I couldn't stop obsessing over it). Makes you smile, makes your heart beat fast, and keeps you thinking about it long after you stop reading.
Overall
One of my all-time favorites along with Kurohime. An absolute must-read. I enjoyed it immensely and you probably will, too.