An amastigote is a cell that does not have a visible external flagella

Flagellum

A flagellum is a tail-like projection that protrudes from the cell body of certain prokaryotic and eukaryotic cells, and plays the dual role of locomotion and sense organ, being sensitive to chemicals and temperatures outside the cell. There are some notable differences between prokaryotic and...

 or cilia

Cilium

A cilium is an organelle found in eukaryotic cells. Cilia are slender protuberances that project from the much larger cell body....

. The term is used mainly to describe a certain phase in the life-cycle of trypanosome protozoans. It is also called the leishmanial stage, since in Leishmania

Leishmania

Leishmania is a genus of Trypanosomatid protozoa, and is the parasite responsible for the disease leishmaniasis. It is spread through sandflies of the genus Phlebotomus in the Old World, and of the genus Lutzomyia in the New World. Their primary hosts are vertebrates; Leishmania commonly infects...

it is the form the parasite takes in the vertebrate host, but occurs in all trypanosome genera.