It is commonly believed that the original root word of 'tattoo' comes from the Samoan or the Tahitian word tatau, meaning to mark or strike twice (the latter referring to traditional methods of applying the designs). The first syllable "ta", meaning "hand", is repeated twice as an onomatopoeic reference to the repetitive nature of the action, and the final syllable "U" translates to "color". The instrument used to pierce the skin in Polynesian tattooing is called a hahau, the syllable "ha" meaning to "strike or pierce".
The OED gives the etymology of tattoo as "In 18th c. tattaow, tattow. From Polynesian (Tahitian, Samoan, Tongan, etc.) tatau. In Marquesan, tatu." The first closest known usage of the word in English was recorded in the diary of Captain James Cook in 1769 during his voyage to the Marquesas Islands. The text reads, “...they print signs on people’s body and call this tattaw”, referring to the Polynesian customs. Sailors on the voyage later introduced both the word and reintroduced the concept of tattooing to Europe.
This is not to be confused with the origins of the word for the military drumbeat — see military tattoo. In this case, the English word tattoo is derived from the Dutch word Taptoe (OED).