High-flyers, sometimes spelled high-fliers, are people who have achieved notable success, especially those who have become successful more quickly than is normal. The term is also used to describe speculative stock that has reached a high price in a short time.
We might expect this term to have originated in the world of aviation. In a way that's correct. The phrase does in fact predate the invention of planes/balloons by some hundreds of years, but there is an avian connection - if we recall that the word aviation derives from the Latin name for birds - avis. The first known citation of it in print is in Richard Harvey's diatribe Plaine Perceuall the peace-maker of England, 1590:
"Men haue great desire to be compted [regarded as] high fliers and deepe swimmers."
When looking for the origin of the term we need to take account of its change in meaning over time. When coined in the 16th century it wasn't used admiringly to refer to someone who had achieved success, but critically about someone who unwisely aspired to achievements beyond their talents. We still retain a version of the phrase with that meaning - high-flown, which we reserve for critical judgments of people who are extravagantly ambitious and bombastic. These are of course exactly the character faults that were ascribed to Icarus, the figure of Greek mythology who ignored his father's warnings not to use his homemade wax and feather wings to fly too close to the Sun, resulting in the inevitable crash to Earth. It is clear that, until the late 17th century at least, high-flyers were directly equated with Icarus; for example, William Chilcot's Practical treatise concerning evil thoughts, 1698:
"These highflyers, when they are in their altitudes, suddenly their waxen wings melt, and down they fall headlong."