Late in the Sixties, the stock market was riding a bubble. Rapid trading in mutual funds drove the market upward, and the opportunity for quick riches led people to buy volumes of stock based on tips or rumors rather on reliable information. (Sound familiar?) The bubble finally burst in the early 1970s, but until then, the rapid-growth stocks were nicknamed "go-go stocks" ("Go! Go! Go!" etc.) -- the rare opposite being "no-go."
Somewhere in that brief era of plentiful wealth, "go-go" also became synonymous with dancing -- more specifically, dancing by yourself in such a manner as to attract as much attention to yourself as possible. The two-partner dancing that started with ballroom and continued through the 1930s and 1940s with swing evolved into rock and roll dancing in the 1950s, and then crashed head-first into go-go. Blame the sexual revolution and its philosophy of free love, if you must lay the blame somewhere. Partner dancing wasn't dead, but it was suddenly outnumbered. (Sometime later the two joined up and spawned the love child of disco dancing. God help us all.)
Go-go boots, plastic go-go rings, go-go dresses, and every other fashion accessory that people now associate with the 1960s got their names from the go-go dances they were worn to. Suffixing anything with the words "A Go-Go" meant it was about dancing or a dance party, although today it usually means it's about the 1960s and the lifestyle it popularized. Meanwhile, "go-go dancing" today retains its original meaning of dancing by oneself, usually for exhibitionist purposes and often as part of an exotic or strip club show.
You'll still hear it used to talk about the stock market from time to time, but typically only in regards to that era. The mental image of the boots and miniskirts is just too overwhelming.