As I like to think of it, flavor profiles are a blend of basic spices in a basic ratio that impart a specific signature flavor. I have heard some people speak of flavor profiles in terms of a balance of the 5 basic flavors, sweet, salty, sour, bitter, umami, but honestly I do not think of that as a "flavor profile", because in general everyone is looking for a balance of those flavors when concentrating on that aspect of flavor.
Examples of basic flavor profiles are "French Onion Soup", which could in essence be boiled down to beef bouillon and onion flavor. That is a very primitive example. If you taste many different rubs, you will find there are a few various "flavor profiles" that you cna use in a sense to group them together into similarly flavored categories to a certain degree. That is not to say all rubs follow a finite set of flavor profiles, but you will find groups of them that are very similar because they tend to use the same ingredients between them in similar ratios.
Hope this helps.