When we borrowed impetuous in the late 14th century, we used it of people and their actions. About a hundred years later, we added another sense to describe physical things like wind or storms or seas—this second sense we don't use much anymore. The word comes via Anglo-French from Late Latin impetuosus, which is from impetus. Latin impetus (which of course gave us our own impetus, meaning "driving force") essentially means "assault," but it also has figurative senses ranging from "violence" to "ardor." Our impetuous has a similar range of meaning, from "violent" to "passionate." It also carries the suggestion of impulsiveness. Often, we put a light touch on the word, as when we refer—somewhat longingly, perhaps—to our "impetuous youth."

What, and Who, Gets Described as Impetuous

Impetuous is often applied to various kinds of behavior, and to the people who exhibit that behavior. Impetuous behavior is often impulsive behavior: the impetuous among us act without thinking long and hard about the consequences of their actions. They are rash and reckless:

The new monarch—the first grandchild of Queen Victoria and Prince Albert—was boastful, arrogant and impetuous. He spent most of his waking hours talking, arguing, shouting, predicting, threatening and generally unbosoming himself of his latest preoccupations to whomever happened to be within earshot. Even when he made the utmost effort to restrain himself, the indiscretions kept slipping out.
— Christopher Clark and Andrew Preston, The New Statesman, 1 Nov. 2016

His characters … often explicitly and conspicuously [reject] advice to take time, find out more, gather information, test assumptions, or consider alternative courses of action. Such impetuous decisions usually lead to greater calamity.
— Edith Hall, in A Companion to Sophocles, 2012

If Nicholas be not always found to be blameless or agreeable, he is not always intended to appear so. He is a young man of an impetuous temper and of little or no experience; and I saw no reason why such a hero should be lifted out of nature.
— Charles Dickens, preface to Nicholas Nickleby, 1839

Passion, ever an inspiration for impetuous behavior, is also often implied, as those guided by the heart take ill-considered action:

This isn't the most historically faithful examination of the relationship between Henry [VIII] and Anne Boleyn, the singular woman who managed to control him, however briefly. But the drama deftly humanizes this impetuous pair as it explores the circumstances that brought them together and drove them apart.
— Tim Smith, The Baltimore Sun, 27, Oct. 2016

The word is, especially in literature, sometimes applied to those that can't, in fact, do much considering at all, ill or otherwise:

A wide plain, where the broadening Floss hurries on between its green banks to the sea, and the loving tide, rushing to meet it, checks its passage with an impetuous embrace.
— George Eliot, The Mill on the Floss, 1860

Sylvie burst in all impetuous, sprang to my lap, and with her paws at my neck, and her little nose and tongue somewhat overpoweringly busy about my face, mouth, and eyes, flourished her bushy tail over the desk, and scattered books and papers far and wide.
— Charlotte Brontë, Villette, 1853

The impulsiveness of an impetuous human is here imagined to exist in a river and a dog. This too is standard use, and not an example of writers being impetuous with word choice.