In most states the default employment relationship is at-will: either party may end it at any time, with or without notice, for any reason that is not unlawful.
The word carrying the weight is lawful. At-will is not a defence to terminating someone because of a protected characteristic, in retaliation for protected activity, for refusing to break the law, or for exercising a statutory right. It is a default rule about notice and cause, not permission.
It is also defeasible. An employment contract for a term, a collective bargaining agreement, and in some states a handbook or a course of conduct that creates a just-cause expectation can all displace it. Employers who circulate progressive discipline policies sometimes create the expectation they were trying to avoid.
The practical consequence is that “we can fire anyone at any time” is a dangerous belief. The question in almost every wrongful termination case is not whether the employer had the right to terminate, but whether the actual reason was one of the unlawful ones — and that is proved by documents, timing and comparators rather than by the at-will rule.