A hanko is a stamp used by japanese people in place of a signature. The stamp itself can be make of wood, or horn or even rubber and usually has the kanji of the person's last name on it, enclosed in a circle. Round hanko are used primarily by individuals, square ones are used by companies.
The hanko is a small column, about 5cm long and 12mm in diameter. It is kept in a hard case with stamp pad of red ink. Anywhere that you'd usually sign your name, you can also stamp instead with your hanko. (e.g. checks, contracts). Something as big as buying a house might require a hanko with a first and a last name on it, and would be registered with the government.