Hi there! I'm going to copy/paste a response I cave to a similar question a few months ago. The short answer is that observational comedy certainly existed as part of the routines of performers in pre-modern societies, but the modern medium of a stand-up comedy show developed very recently. If you have any further questions, I'll respond when I can.

Other nations have their own traditions but in the United States, stand-up as we know it today (one person standing alone on a stage telling jokes to a live audience for an extended period of time) grew out of the minstrel shows of the 19th Century. Minstrel shows are not performed or even discussed very often anymore because they ridiculed black Americans before, during, and after the Civil War. Blackface minstrelsy was the first distinctly American theatrical form and it did not fall completely out of fashion until well into the 20th Century.

Thomas Dartmouth "Daddy" Rice is often cited as the grandfather of American stand-up. As one of the acts in his minstrel show, Rice would wear blackface and ascend the stage alone in the persona of a character called Jim Crow. Rice would sing, dance, tell jokes, and improvise while speaking directly to the audience thus making him the first known stand-up comedian in the modern sense of the term. Rice's performances were very popular and soon the monologue as Jim Crow was a staple in minstrel shows.

Stand-up may have been born in a minstrel show, but it grew up in Vaudeville. Unlike minstrelsy, Vaudeville featured variety acts and regularly packed urban crowds into large theaters. Before the invention of the microphone, comic subtlety would be lost on a large crowd so the performers would use slapstick, snappy one-liners, exaggerated movements, and physical comedy to entertain the crowds. Vaudeville comedians were not always free to speak about controversial subjects, however. Saying the wrong thing about the wrong person could be career suicide during this period. That is, until the day Will Rogers came to New York City.

Will Rogers was at Madison Square Garden when a steer crawled out of the arena and began to climb into the stands. Rogers roped the steer and led it back to the arena. The crowd was absolutely delighted. Rogers made the front page of the New York Times, and his career as a stunt roper/comedian was set.

Will Rogers' skill with a lasso is legendary and his performances were absolutely hilarious. They included biting political commentary that targeted some of the most powerful people in America, but Rogers always got away with it due to his immense popularity and carefully crafted image as the quintessential American cowboy.

After the invention of the microphone, many of the most famous Vaudeville comedians transitioned to radio. Jack Benny, Bob Hope, George Burns and Gracie Allen, Abbott and Costello, and others were now being heard by audiences that numbered in the millions.

With the age of television, variety shows like "The Tonight Show" and "The Ed Sullivan Show" transformed (or perhaps gave birth to) modern stand-up comedy for a live audience by broadcasting it into millions of living rooms. Then came the final ingredient.

One night in 1959 "The Steve Allen Show" featured a comic calling himself Lenny Bruce who would essentially remove all limits on what could be discussed in a stand-up routine. Lenny Bruce's comedy was raw, raunchy, and allowed people to find humor in topics that were considered taboo in polite conversation. The story of Lenny Bruce is inspiring, heartbreaking, infuriating, and much too long to type out here. Suffice it to say that after Lenny Bruce, just about anything could be discussed in an American stand-up comedy routine so long as the material was truly funny. He was immensely influential and I often hear him cited as the root of our modern concept of the adult stand-up comedy show. Lenny Bruce died in 1966. That same year, "stand-up" was recognized as a word by the Oxford English Dictionary.