The word kajillion is an informal and nonstandard term that is used colloquially to denote an extremely large or indefinite number. It is not typically found in formal writing or in dictionaries.
It is believed that kajillion is a playful invention meant to exaggerate and emphasize the magnitude or indefiniteness of a number. The prefix kaj- is added to the ending -illion (which itself is derived from the Latin numerical prefix illi-, meaning one thousand), creating a whimsical and exaggerated term. It is likely that kajillion originated as a creative and humorous extension of words such as million, billion, or trillion.