Colorways/colourways are the range of colours in which yarns are available. (The internet reliably informs me that the word is also used to describe the colours in which clothing products are available, but we're going to focus on yarn here.)
Yarns come in a massive array of shades and hues, and manufacturers often give their colourways unique names that don't necessarily spell out what colour we're actually talking about. The Texas-based yarn company Madelinetosh offers its yarns in colourways such as Edison Bulb (a bright neon yellow) and Molly Ringwald (it's pink, get it?). Other companies — Noro is one example — don't really name their colourways, but give them ID numbers instead.
A colourway is also not necessarily confined to one single colour; variegated yarn weaves multiple hues into a ball or skein, and self-striping yarns are designed to alternate between different colours at a consistent rate when knit over a specific width.
Hunting for colourways is one of the most fun parts of yarn shopping, provided you don't get too stressed about it. While waiting to pay at my local yarn store earlier this year, I overheard a woman telling a clerk that while they appeared to have "lemon" and "banana" yellows in a particular yarn weight, "what I really need is a sunshine yellow." Ravelry enables users to search other users' projects by colourway so they can see how finished items look in different shades. This is particularly useful when you want to see how a variegated yarn looks when knitted up.
Yarns in the same colourway can vary greatly in shade and hue depending on their dye lot. It is also difficult to gauge how a colourway will look in the flesh based on photos on a website, so be wary.
* This was a rescue of a nodeshell titled using American spelling. My writeups have always used British/Canadian spellings. Don't mind the cognitive dissonance.