The word television is older than any television. It was in print decades before anyone could watch a moving picture sent through the air.
The coinage is credited to Constantin Perskyi, professor of electricity at the Artillery Academy in St. Petersburg. In August 1900 he gave a paper at an international electricity congress held during the Paris World's Fair. The paper was in French, and it used the word télévision for the idea of seeing at a distance. Wikipedia notes that the term only caught on in Russia itself a few years later.
English picked the word up quickly. Etymonline's earliest English example is from 1907, in Windsor Magazine, which assured readers that "television is not impossible in theory." At that point the word named a hope, not a machine. Etymonline also records earlier attempts at a name for the same idea: telephote in 1880 and televista in 1904. Neither stuck.
The parts are simple. Tele- is Greek for "far, far off." Vision comes from Latin visio, "sight." Put together, they mean "far sight."
That mix of Greek and Latin is what bothered people. Linguist Peter Trudgill writes that some early critics called it a "mongrel" word. The editor of the Manchester Guardian, C. P. Scott, is supposed to have said something like "The word is half Greek and half Latin. No good can come of it!" Trudgill hedges it with "supposed" and "something like."
The complaint went nowhere. Trudgill notes that French, Finnish, Polish and Albanian all use a version of the same hybrid. Icelandic and Faroese went their own way with sjónvarp, from native words for "sight" and "throwing, projection."
English then started cutting the word down. Etymonline dates the British "telly" to 1942, "TV" to 1948 and the spelling "tee-vee" to 1949. Once the device was in every home, the long Greek and Latin name was too much to say.