This is a medical root term that originates from the Greek and means "vessel", as in a "container". The term is commonly misunderstood to mean "artery". The original meanings of the term in early Greek and Roman medicine where multiple. It was Lorenz Heister (1683-1758) who first used the term in its modern meaning. Applications of this root term include:

Angiology: Study of vessels
Angioma: Vessel tumor or mass, usually referred to a malformation of knotted vessels. The plural form is "angiomata"
Angioplasty: Reshaping of a vessel
Angiitis: Inflammation of a vessel. Note the double "i" in the word. This is the correct form of the term. "Angitis" is not correct!
Angiogenesis: Creation or generation of vessels
Neoangiogenesis: The prefix [neo-] means [new], therefore the term means "creation or generation of new vessels"
Cholangiogram: The prefix [chol-] means "bile", while the suffix [-ogram] means "examination of". A [cholangiogram] is the "examination of a bile vessel"
Cineangiogram: The prefix [cine-] means "movement", although we use it to mean "movie", while the suffix [-ogram] means "examination of". A [cineangiogram] is the "examination of a vessel in movement"