A colloquial term (i.e. bit of jargon) used to refer to a bacterial culture that has been allowed to grow over an approximately 12 hour period, that usually spans the afternoon of the previous day to the present morning. In most cases, an overnight is initiated by inoculating an Erlenmeyer flask containing culture broth –– a yummy soup for bacteria so that they can grow, also known as medium –– and placed in an incubator. If it is an aerobic bacteria species then the contents of the flask should be swirled vigorously to keep a sufficiently high concentration of oxygen dissolved in the broth. The broth is so full of nutrients that one must be careful to prevent contamination of the overnight by other bacteria or fungi. Consequently, all of the above is usually done in close proximity to a lit Bunsen burner, that creates a rising current of heated air that prevents airborne particles from landing in the broth. That's the general idea, anyhow.
Over time, one cultivates a keen eye for a healthy overnight. It should be cloudy or milky because of the sheer abundance of bacteria. You only need to inoculate the broth with the amount of a bacterial colony that can be picked up on the tip of a pin, to obtain billions of cells per mL in the overnight. Occasionally, however, cells somehow fail to be transferred and the overnight will fail. This happens to be the annoying circumstance that prompts me to write this long-winded passage on the science of making overnights. It is a particularily unfortunate event because having no overnight prevents you from performing any experiments for the day, and leads to reading papers and making wu on E2. *sigh*