Well, I can't give an in depth review of the importance of coal, but I can say this-

1: Coal was important because it was commonly found in Europe and abroad, but where as something like oil took a fair amount of processing to take from initial substance to a workable product (mining might seem expensive, but so was tracking a whale on the other side of the globe, or traveling to the icy waters of the north to hunt seals, and if you wanted to use it for something other than heating and lighting, you needed to refine whatever you gathered. The infrastructure simply wasn't there to make much of oil and oil products till the start of the 20th century) coal was fairly simple. There was such a thing as poor quality coal though. Forget what they called it- brown coal or lignite or peat coal or something- but basically it didn't burn as well and was a lot messier.

2: Coal was important because it could attain, and hold very high temperatures. The development of pre-industrial steel owes a lot to coal. The wider industrial revolution was entirely dependent on coal, especially high quality coal. One of the reasons that Britain was a major player in the Industrial Revolution was because of it's ability to gather large amounts of it. Coal was a primary indicator of a nation's wealth throughout the Industrial Revolution.

3: Coal isn't a rock. And while it's purely conjecture, I'm sure someone who had seen mined coal, and had ever worked a fire would have looked at the embers after a fire, looked at coal, and drawn the connection. Regardless, the answer for the earliest usage of coal is lost to history. We have reason to believe the Chinese were mining it up as early as 1000 BCE to smelt copper. We've found trace amounts of coal used in bronze age funeral pyres in the British Isles, which was probably harvested from outcroppings. The Romans extracted coal from Germany (Rhineland, specifically) for use in iron smelting.

Coal is important because its easy to work with. Compared to other common heat sources you simply didn't get much simpler than the usage of coal from initial harvesting to final product without giving something up. Wood might have been replenish-able and (arguably) easier to get, but it didn't burn as hot. Oil may have been able to burn hotter and / or longer, but was also far more involved to harvest.