Ezra leaves his nice home in Babylon and helps reassemble the shattered pieces of Israel into a new nation, personally instructing the people in the Laws of Moses. He's a stickler for the rules, making people divorce their foreign wives and send away their half-foreign children.
There isn't much characterization in Ezra; we don't get to learn too much about him beyond a few basic facts. Whereas in Exodus we get to learn that Moses has a speech impediment and get to see his intimate relationship with God, Ezra is just the guy who shows up at a critical time in Jewish history and gets the job done.
We know he's a scribe, someone who copies books for a living. (He's credited by some with writing the Biblical books of Chronicles and Nehemiah in addition to Ezra.) He's descended from a high priest named Seraiah who traces his lineage all the way back to Aaron, Moses's brother and first high priest of Israel. This is just about the first thing we learn about Ezra, and it right away establishes that he's got some major-league cred. He lives in Babylon during the reign of the Persian Emperor Artaxerxes, who seems to be pretty impressed with him and authorizes him to do just about anything he wants:
And you, Ezra, according to the God-given wisdom you possess, appoint magistrates and judges who may judge all the people in the province Beyond the River who know the laws of your God; and you shall teach those who do not know them. All who will not obey the law of your God and the law of the king, let judgment be strictly executed on them, whether for death or for banishment or for confiscation of their goods or for imprisonment. (NRSV 7:25-26)
Ezra's got one goal: to remind the Jews that they need to get serious about observing the laws of Moses:
For Ezra had set his heart to study the law of the LORD, and to do it, and to teach the statutes and ordinances in Israel. (NRSV 7:10)
We also see that he's a man of faith. He credits God with inclining the heart of the king to let him return to Judea:
Blessed be the LORD, the God of our ancestors, who put such a thing as this into the heart of the king to glorify the house of the LORD in Jerusalem, and who extended to me steadfast love before the king and his counselors, and before all the king's mighty officers. I took courage, for the hand of the LORD my God was upon me, and I gathered leaders from Israel to go up with me. (NRSV 7:27-28)
He has faith in the power of prayer and fasting:
Then I proclaimed a fast there, at the river Ahava, that we might deny ourselves before our God, to seek from him a safe journey for ourselves, our children, and all our possessions. (NRSV 8:21)
Ezra arrives home to find things in pretty bad shape. Everyone's clueless about God's laws. Worst of all, he discovers that the men have been intermarrying with non-Israelite women, and he's shocked. Shocked.
When I heard this, I tore my garment and my mantle, and pulled hair from my head and beard, and sat appalled. Then all who trembled at the words of the God of Israel, because of the faithlessness of the returned exiles, gathered around me while I sat appalled until the evening sacrifice. (NRSV 9:3-4)
He knows what he has to do. After staying up and fasting all night he sends an order for everyone to gather in Jerusalem and lays down the law. He chooses priests to investigate the situation and discover who has married a foreigner. Once the offenders are discovered, they're forced to send away their foreign wives and children. Ouch.
We learn in the Book of Nehemiah that Ezra is super-diligent in teaching the laws to the people. He reads all day and hires the Levites to explain whatever the people can't understand. They probably have to translate from the Hebrew to Aramaic, since many of the people don't understand Hebrew. When Ezra reads to the people from The Law of Moses, he emphasizes their past failures to be obedient:
Many years you were patient with them, and warned them by your spirit through your prophets; yet they would not listen. Therefore you handed them over to the peoples of the lands. Nevertheless, in your great mercies you did not make an end of them or forsake them, for you are a gracious and merciful God. (NRSV Nehemiah 9:30-31)
He's determined to make a fresh start, saying, in effect, yeah, mistakes were made. But it'll be different this time, with God's help.
In fact, the name Ezra means, "help."