Definition: The term "signature hole" is nothing more than a marketing term, although it's now been adopted by golf media and fans. The "signature hole" at a golf course is the one hole that the course has decided is most aesthetically pleasing and most photogenic. A signature hole may or may not be representative of the golf course as a whole, but because it is so pretty or dramatic it is the hole featured in the golf course's advertising and marketing efforts.
And since that becomes the hole area golfers are most familiar with, the signature hole then gets talked about by golf media and fans.
Some courses go even farther these days and claim two signature holes. As in: "Our course is so good, we couldn't pick just one!" Within the next few years, expect to see a golf course advertising itself like this: "Come play our course - it's so good we have eighteen signature holes!"