Carelessness that the law treats as a legal wrong because it fell below the level of care a reasonable person owed to someone else.
Negligence is the legal name for carelessness that causes harm. It is not the same as being clumsy or unlucky: to hold someone legally responsible, an injured person generally has to establish four separate things - that the other person owed them a duty to be careful, that the person fell short of that duty, that the shortfall actually caused the harm, and that there was real harm to compensate.
The "duty to be careful" is measured against a standard, not against the person's own intentions. Someone can be entirely well-meaning and still be negligent. Conversely, an accident that nobody could reasonably have prevented is usually not negligence at all, which is why "there was an accident" and "someone is liable" are different questions.
Professionals are held to the standard of their profession rather than the standard of an ordinary person, which is why claims against doctors, accountants or lawyers usually require testimony from someone in the same field about what competent practice required.
Most people consult a lawyer about negligence after an injury, when an insurer has made an offer or has denied responsibility. The two questions a lawyer is answering are whether the four elements can actually be established with available evidence, and what the harm is worth - and those are separate questions that non-lawyers frequently merge.
Choose your state. Each link opens the directory page for the city in that state with the most currently published law firms in this practice area; a +n beside the city is how many other cities in the state also have one. The list is generated when this page loads, so a state whose listings have lapsed drops out rather than becoming a dead link.