Let me first say, Timothy Zahn is a brilliant author. His Star Wars Trilogy he wrote is--and always will be--my favorite novels. Zahn gives you the image that Star Wars is NOT child's play--as some of the movies are. This is some very serious reading with multiple well-developed plots.
The first volume, Heir to the Empire, takes place five years after Return of the Jedi. The Rebel Alliance--now known as the New Republic - have driven out the remnants of the Imperials--who have become but a shadow of the once mighty "Empire". Princess Leia and Han Solo are married--and expecting Jedi Twins. And Luke Skywalker has become the first in a new line of Jedi Knights. But all is not well as it seems. A mysterious Warlord--a Grand Admiral at that--rises to take command of the shattered Imperial Fleet. Meanwhile, the New Republic is but a young government struggling from internal politics and a shortage of ships. Will they be able to survive this new threat?
As I previously mentioned this story is multi-faceted and marvelously weaves together the different plots perfectly. But the true highlight is the introduction of new characters into the Star Wars universe.
Many call these three novels, the "Thrawn Trilogy", and rightfully so. Grand Admiral Thrawn is the true star. Despite being the "enemy", you have to love this man--or at least appreciate his insight. He is cruel when he has to be--but he doesn't kill for pleasure. He is calm, cool and collected at all times. He is the master strategist.
Along the way, Thrawn discovers a Mad "dark Jedi" clone - Joruus C'boath. They form an uneasy alliance--both using each other as a means to an end. Thrawn needs the power of a Jedi to complete his war machine, while C'Boath needs Thrawn to hand him Luke Skywalker in order to train him the "true" ways of the Jedi. As Thrawn quickly find outs, C'Boath is a complete lunatic. And in being a lunatic, he was a well-developed character. The readers will quickly side with Thrawn here.
Heir to the Empire--unlike all previous Star Wars stories--deal with the politics and the inner government workings. The government in question here is, of course, the New Republic. One reason why the story deals heavily on this subject is because Princess Leia Organa Solo is now a Senator. Familiar--but previously underdeveloped--characters are also on the Senate Counsel. Mon Mothma and Admiral Akbar. While both had bit parts in Return of the Jedi, Zahn completely develops them for future use. We are also introduced to Borsk Fey'la--the Bothan. Yes, Zahn took a single line from Jedi, "Many Bothans have died...", and developed this now important race in a fantastic way. Fey'la--being at the front and center-- is a completely unlikable man--if we can call him that; but ultimately, he is misguided--rather than a villain. Fey'la's plot reaches a pinnacle in Volume II of this series.
On of the last--major--characters introduced are Talon Karrde and Mara Jade. Once the organization of Jabba the Hutt collapsed, the smuggler arena became an open forum. Quickly, Talon Karrde found himself one step ahead of his competitors. Unlike Jabba, Karrde is private, mysterious, practical, and calculating. Karrde is easily my favorite addition to the Star Wars universe. Yes, even more notable than Thrawn. Unfortunately, he will find himself in the middle of the New Republic/Imperial struggle. This proves to be a hindrance to him as he desperately tries to remain neutral. His assistant is the fiery Mara Jade. She is perhaps Zahn's single most important addition--impact-wise--to the Star Wars universe. Her character is exponentially developed as each novel progresses. You will never see such a bitter and sarcastic woman like Mara.
I believe the reason that these books excel--compared to the rest of the Expanded Star Wars universe ("expanded" does not include the movies) are because they dwell more on the political side of Star Wars, the bureaucracy. They are not simple books about Luke and his continual training to be a Jedi. That is what was accomplished during the movies. And of course, the races, planets, plots and characters written by Thrawn are absolutely incredible. This is clearly not child's play! In fact, most children under 12 will not appreciate some of the finer nuances of the story.
In short, read Heir to the Empire. I do not know how to be any more clearer.