Röttgen Pietà, c. 1300-25, painted wood. Source.
The term "Middle Ages" refers to the period after the fall of the Roman empire up until the beginnings of the Renaissance - it's the time "in the middle" of these two "great" periods.
Both the terms "Middle Ages" and "Dark Ages" are somewhat derogatory terms implying that the period had little to offer compared to the great accomplishments of the Romans and the Renaissance artists. The Italian poet and scholar Petrarch coined the term "Dark Ages" because he believed it to be a period of intellectual darkness due to the loss of Classical learning. The Dark Ages, then, referred to the period between the end of Classical Antiquity and the renewed interest in Classical learning that developed in the Renaissance.
To think of the Medieval period in this way greatly undermines the accomplishments of the era. During the Middle Ages we see the rise of universities, the establishment of European countries, ecclesiastical reform, and the rise of the tourism industry. In art, we see the creation of lavish cathedrals, sculpture, painted manuscripts, textiles, and jewelry.
Much of the artwork made at this time was created for the Church. This is a time when Christianity flourished, and the relatively new religious philosophy was responsible for a great shift in the style and manner of visual art created.
When the Roman empire fell, it split into an "East" and a "West." In the East, the Byzantine empire remained strong from its capital in Constantinople (modern-day Istanbul, Turkey) and eventually developed the Eastern Orthodox Church. The West, however, fragmented into smaller political entities that would lead to the modern-day boundaries of western European countries. Catholicism would be the dominant form of Christianity in the West.
Painting Techniques:
Khan Academy: Tempera paint (video - 11:48)
Early Christian Art:
Khan Academy: Early Christian Art (reading)
Khan Academy: Early Christian art and architecture after Constantine (reading)
Byzantine Art:
Khan Academy: San Vitale, Ravenna (video - 10:18)