The Transformation of a "Wee Little Man"

If you attended Sunday School as a child you probably learned the following song:  
Zacchaeus was a wee little man and a wee little man was he. 
He climbed up in a sycamore tree for the Lord he wanted to see.
And as the Savior passed that way he looked up in the tree.
And he said, "Zacchaeus! You come down from that tree!" 
For I'm going to your house today.
So, who was Zaccheus, really,  and why was he so interested in Jesus that he decided to do such an undignified thing as climb a tree? And what happened to him after Jesus singled him out and he came down from that tree? And what does that have to do with you and me?