Domestic sheep are descended from Mouflon which still exist today. Mouflon do not have fluffy wool like modern sheep. They do however have a winter coat which they will grow if the temperature drops low enough that they shed each spring.

Early mouflon were probably treated similarly to the ibex (the ancestor of modern goats) when first domesticated. They were smallish hoofed mammals raised for their meat. At some point, a mouflon was born with a genetic mutation that made their winter coats longer and woolier. Not quite to the point we see them today, but definitely shaggier. Early shepherds realized that this hair could be collected and spun into threads.

At first, this wool was likely seen as a bonus. Shepherds would be raising the sheep anyway and as the sheep matured and fattened up, their wool could be collected and traded or used each spring. This made woolier sheep more valuable because each animal could provide extra value throughout its life time. This encouraged shepherds to select for the wooliest sheep and over time the wool grew thicker and longer, the mouflon began producing it year round instead of only in colder months and soon the value of the wool greatly outpaced the value of the meat, especially in colder climates.

As a result, the main use of sheep shifted from a source of food to a source of wealth.

Typically, animals like sheep and goats were raised in areas with less arable soil. Their native habitats were arid, mountainous and rocky and unsuitable for farming. Sheep and goats could graze on the coarse grasses and navigate the rocky terrain, and so humans could use them to extract sustenance out of a landscape that was otherwise unsuitable for growing crops.

Over time, herders selected their animals for different traits. Modern goats often produce milk and are capable of consuming many different foods. They don't require a ton of space and are ideal for being raised by a single family in small numbers.

Sheep herding followed a different path; they began to be raised on otherwise arable land because the value of their wool would enable a shepherd to buy more than enough food to support a family.