Some time ago there was a German progressive rock magazine that called itself Sophisticated Rock Magazine and maybe this is a far better name for the style of music on these pages. What counts is that the simple verse-chorus format and the 3-4 minute single length is not enough for some artists. Some bands want to consider also atmosphere in their music, some want their music to be dynamic, some want to incorporate breaks, tempo changes and varying signatures and all of that leads to longer, more elaborate song structures. Whether these bands succeed in this, is a totally different question.
Complex music also gives rise to more complex and inventive arrangements and often the use of "special" instruments. Basically however the line-up of a prog band consists of guitar, drum, bass and keyboards, usually with but sometimes without vocals. Especially the role of keyboards in symphonic rock (a subgenre of progressive rock) is of large import. Instruments like the Hammond B-3 organ and the Mellotron have a legendary status. It seems that a band using these instruments a lot can do no wrong in the eyes of many reviewers.
Sicne the nineties progressive rock has hardened, as almost anywhere else in the music, mostly due to the advent of progressive metal. I also devote part of my pages to that "subgenre" involving bands and derivatives of bands such as Queensryche, Dream Theater, Savatage, Fates Warning and Rhapsody. However, for me to like this branch of music I demand not only complexity in the music, but also melody. There is also a slew of bands since the 2000's like Leprous, Tesseract and what have you that stretches the boundaries even further.
It is my opinion that the best thing to do is to name a number of artists that are more or less responsible for the genre, although many of these artists will not be of the same opinion: ELP, Genesis, Yes, King Crimson, Gentle Giant, Henry Cow, Magma, Van Der Graaf Generator, Marillion, Rush, Saga, Soft Machine are to me the most well-known advertisers/originists of the style. If you want to have some more recent successful bands in the genre, think of Dream Theater, Flower Kings, Spock's Beard, IQ, Pendragon and Ayreon. Of course, many of the older bands also still exist, but compared to their so called "golden era" many changes have occurred: some bands have continued to renew and refresh themselves, some are bringing watered down versions of their old music and some have plain continued doing what they do best.