The word medieval has its origins in the Latin term medium aevum ("middle age"), and first came into use in the 19th century, although the idea of a middle age had been around for several hundred years. At that time, scholars considered the medieval period to follow the fall of the Roman Empire and precede the Renaissance. This medieval era had long been ignored as unimportant compared to the time periods it bridged.
Since the 19th century, definitions of the medieval era (as well as when and whether or not Rome "fell" and the view of "The Renaissance" as a distinct time period) have varied greatly. Most modern scholars consider the medieval period to last from approximately the 5th century to the 15th century C.E. -- from the end of the Ancient period to the beginning of the Early Modern Age. Of course, the parameters of all three eras are fluid and depend on which historians you consult.
The attitudes scholars have taken toward medieval times have evolved over the centuries. Initially, the Middle Ages were dismissed as a "dark age" of brutality and ignorance, but later scholars began to appreciate medieval architecture, medieval philosophy, and the particular brand of religious devotion that caused some 19th-century scholars to label the era "The Age of Faith." Medieval historians of the 20th century recognized some seminal developments in legal history, technology, economics, and education that took place during the medieval era. Many of our modern western moral viewpoints, some medievalists would argue today, have their origin (if not their full fruition) in medieval times, including the value of all human life, the merit of all social classes and the right of the individual to self-determination.
The word "medieval" is popularly used to indicate something that is backwards or barbaric, but few who have actually studied the time period would use the term so disparagingly.