Film noir is sometimes used as a catch-all phrase to designate any film from the 1940s or 1950s which has moody black-and-white photography, snappy, cynical dialogue and some sort of crime element in its plot. In the process, the term becomes too vague to be really useful.
Gritty underworld crime dramas have been with us since the early silent era, as has moody expressionistic cinematography, and the private-eye murder mysteries of the early 40s had plenty of snappy, cynical dialogue. But the true film noir didn't emerge until after WWII and it brought something new to Hollywood cinema -- a comprehensive vision of the modern world as a dark, hopeless place, morally compromised at its core.
Underworld crime dramas could be dark, but they always imagined forces of order and decency ready to do battle with and overcome the forces of chaos and destruction. The private eye, for all his cynical talk, had a kind of nobility and honor that he carried with him into the shadowy realms in pursuit of truth and rough justice.
Traditional crime dramas and police or agency procedurals continued on into the post-war era, as did murder mysteries, and though they became inflected with the atmosphere of true films noirs they didn't stake out quite the same territory.
Laura, made during WWII, is one of the most stylish and diverting entertainments ever concocted in Hollywood, and it's regularly classed as an early film noir -- but it's nothing of the kind. The film believes in romance and love, in the triumph of justice and the possibility of knowing the truth about things. In a genuine film noir this sort of faith has been lost.
Still, one can see themes emerging in Laura which will play out more forcefully in film noir. Laura, the film's title character, is an unusually strong and self-reliant woman, emotionally and financially independent. She destroys a weak man who loves her but can't win her -- as does the femme fatale of the post-war noir tradition. But Laura's strength is seen as a positive thing here, not as an insidious threat, and there's a red-blooded man on the scene who can match her strength.
In the post-war noir, something goes wrong with the whole idea of the red-blooded man, who suddenly seems inadequate to the task of engaging a corrupt world or matching the strength of a self-possessed woman. The world, and desire itself, come to seem like streets that dead-end in disaster and oblivion. Some lines from Two Noble Kinsmen, probably by Shakespeare, who co-wrote the play with John Fletcher, anticipates the realm of the film noir nicely:
This world's a city full of straying streets,
And death's the market-place where each one meets.