The Holy Roman Empire was a region in central and western Europe. Its boundaries fluctuated throughout the Middle Ages, and its rulers often used the title "king" instead of "emperor." Through most of the medieval era, the territory that is now Germany made up the bulk of the empire. Parts or all of Austria, Italy, Denmark, France and the Low Countries were also included in the empire at one time or another.
For a general idea of the boundaries of the Holy Roman Empire through the centuries, check out this series of maps.
The exact phrase "Holy Roman Empire" or Sacrum Romanum Imperium wasn't used until the mid-13th century, but the entity goes much further back, and is sometimes considered to have originated with the crowning of Charlemagne as “Charles, most serene Augustus, crowned by God, great and pacific emperor, governing the Roman empire” in 800 C.E. Most scholars regard the true beginning of the Holy Roman Empire to be when Otto the Great reinvigorated the title in 962. From that time forward, the emperors were primarily German, even though they called the empire "Roman." Although often an emperor would be succeeded by his son, officially emperors were elected by German princes, a practice formalized in the 14th century.
The emperors and popes enjoyed, or endured, a complex relationship that would have both far-reaching and long-lasting effects on Christendom. The empire would last, in one form or another, until the early 19th century.