The titles of these two books are the names of Ezra and Nehemiah, the books' supposed authors. However, it's actually pretty tough to say how much of each book was written by the actual historical figures.
People who believe the Bible is historical truth accept that the both books were actually written by their attributed authors. On the other hand, scholars see Ezra as being a composite, composed of different pieces that had been edited together. Nehemiah, however, seems more like a first-person memoir written by Nehemiah, though it may have also undergone editing and alterations. Some commentators believe that Ezra wrote Nehemiah as well. Both books were originally one book, until the early Christian Church Father, Origen, divided them into two separate works (source).