Old-world monkeys had specifically shaped molars, which are called bilophodont molars. Molars are big teeth in the back of the mouth that are used for grinding food and crushing it into small pieces that are easier to digest. They are very diverse in regards to size and shape in different groups of mammals.
The old-world monkeys had molars with two transverse ridges, so the name bilophodont broken down is "bi" which means "two", and "loph" which means "ridge", while "dont" of course means "tooth". So the name "bilophodont" refers to a tooth that has two ridges.