In our timeline, the Industrial Revolution spanned from 1760 to 1820...or 1840, depending on which source we're talking about. Bottom line is, this period in modern history was a pretty big deal, perhaps the biggest. Rather than overload this question with a list of what made the Industrial Revolution such a big deal, let me instead link you to 12 Industrial Revolution Facts that Changed the World.
The incentive that gave rise to our Industrial Revolution was the invention of many products that made the production of cloth less tedious:
Starting in the mid-18th century, innovations like the flying shuttle, the spinning jenny, the water frame and the power loom made weaving cloth and spinning yarn and thread much easier. Producing cloth became faster and required less time and far less human labor.
More efficient, mechanized production meant Britain’s new textile factories could meet the growing demand for cloth both at home and abroad, where the nation’s many overseas colonies provided a captive market for its goods. In addition to textiles, the British iron industry also adopted new innovations.
In this alternate history scenario, the Industrial Revolution began in the Middle Ages. Specifically, either the High (1000-1250) or Late (1250-1500) Middle Ages. But what sorts of circumstances would force any European kingdom within that window to switch from rural to industrial?