Ivory is the same thing as elephant tusks. People used to kill elephants in India and Egypt, Greece, Rome, or China for wine or silk or glass beads. Because ivory had to travel a long way to get to China or Europe, things made of ivory were very expensive. Most things made of ivory have to be pretty small, smaller than an elephant tusk. Often ivory statuettes are curved to fit the curve of the tusk.
But when people wanted to make big statues out of ivory, they sliced the tusk into thin sheets, and then pinned the sheets of ivory to a wooden statue, to make an ivory statue. The statue of Athena in the Parthenon in Greece, for example, was covered with gold and ivory.
(Today it is illegal in all countries to kill elephants for ivory. People sometimes kill elephants for ivory anyway, but you can help stop them by not buying anything made of ivory).
At first most European and Asian artists used Asian ivory, from Indian elephants. But then they realized that African ivory, from East and West coasts of Africa. Until 1300 AD, people in the Byzantine empire who wanted African ivory traded with the African kingdom of Aksum, so that Aksum stayed a Christian kingdom until the 1300s AD.
Ancient and medieval ivories were usually painted in bright colors, to make them look more like real things. Today the paint has faded, so we see the ivories in their natural colors, but not the way the artists intended.
Bibliography and further reading about ivory:
Elephants, Ivory, And Hunters, by Tony Sanchez-Arino (2004).
Elephant: The Animal and Its Ivory in African Culture, by Doran Ross (1995).
Ivory in Greece and the Eastern Mediterranean from the Bronze Age to the Hellenistic Period, edited by J. Lesley Fitton (1993). Each chapter by a different specialist in ancient ivory.