To understand the exotic-seeming etymology of gazebo, you need to understand the Latin suffix -bo. Any verb ending in -o refers to the first person, and -bo is the future tense for the first person. And the root of the word is the English word gaze (as in "I shall see"), making gazebo a linguistic mongrel from two different languages, something that's quite rare. The reason for this appellation was a humorous allusion to how you can gaze out on the surrounding landscape while in a gazebo. Or so we think: there was no explanation provided for its first usage in a 1752 book called New Designs for Chinese Temples. Assuming this is correct, gaze is of Scandinavian origin and was a verb well before a noun: it is likely connected to Old Norse ga, which meant "to heed" (also the source of gawk), from Proto-Indo-European ghowe, "to honor". Other theories for gazebo's etymology include something from Chinese or Arabic- it's all very iffy.
Adam Aleksic, a leading contender for valedictorian of his high school, is a 214-month-old boy with disturbing interests in etymology, vexillology, geography, and law. Adam would like to one day visit Tajikistan and probably isn't spying for the Uzbek government.
The Etymology Nerd