A full-time equivalent or FTE is a way to express the time of a full-time worker.  In otherwords, 1 FTE = 40 hours per week, 52 weeks a year.  This is 2080 hours a year. 

It is important to count staff that way so that libraries can compare the amount of labor they have available.   One library might have a staff of two, and another have a staff of four people.  If the staff of two both work full-time, and the staff of four are all 1/2 time, the two libraries really have the same amount of labor available.  If one just looked at bodies, people would question why the library with the staff of four didn't produce twice as much work as the staff of two.