The spinning jenny originated in the cotton industry, more than the wool industry (though it was used in both).

Originally, cotton (and wool and linen) were carded (combed) by hand, spun by hand and woven by hand.

In 1748, Daniel Bourn in England invented the cylinder carding machine. In the same year, Lewis Paul, also in England, invented the weirdly named "cat carding" machine. Eventually, in 1775, Richard Arkwright, combined principles from both these machines to make his carding machine which became the industry standard.

So, from about 1750, machine carding became more and more common.

Spinning remained a hand process (though assisted by a spinning wheel, rather than employing a drop spindle). The carded fiber, in the form of a sheet of 'fleece', known as a 'sliver', or a 'roving' was held in a pinch between the finger and thumb about 6 inches from the wheel, drawn out about a yard, and then allowed to relax into the revolving spindle which twisted it into a thread.

Spinning had become the bottleneck in the entire textile industry as carding became mechanized, and as the fly-shuttle loom made weaving much more efficient. By 1760, it took 6 spinners to make enough thread to feed one weaver.

The spinning jenny, invented by James Hargreaves in 1764, was still a hand operated machine. It still had a wheel. It replaced the old single, horizontal spindle with 8 upright spindles (later increased to as many as 120). Instead of drawing the roving out by hand, a wooden 'draw bar' was pulled back to draw the eight rovings out, and then slid forward to relax them into the turning spindles to make the twisted thread.

This method was inferior to hand spinning, in that control over the roving and the tension was reduced. The impact was that the thread was generally weaker and less uniform. In fact, jenny-spun thread was generally only used for weft thread, while stronger, hand spun thread remained used for warp thread. The advantage of the spinning jenny was that 8x the thread (later up to 120x the thread) could be produced for the same labor.

In 1769, Richard Arkwright improved on the spinning jenny by adding rollers, which allowed stronger thread to be produced.

In about 1780, Samuel Crompton modified the spinning jenny into the 'spinning mule' through the addition of allowing the distance between the wheel and spindles to increase and decrease on rollers, giving a much better adjustment to the tension of the thread. This finally allowed mechanized spinning to truly match or exceed the quality of hand spun thread.

Source: http://saltofamerica.com/contents/displayArticle.aspx?19_271