A drawl is a distinctively slow, drawn-out way of talking that's especially common in the US south. A writer might describe a cowboy as speaking in a lazy drawl.
A drawl tends to lengthen and extend vowel sounds in particular, so that words like "pet" or "pen" might be pronounced with two syllables, rather than one short one. While the Southern states are best known for inhabitants with drawls, Australian and New Zealand natives are also sometimes said to drawl. The word probably stems from the Dutch dralen, "delay" or "linger."