Such tiny computers (or "smart dust") will have "tiny CPUs that run programs on a skeleton operating system and be able to access equally small banks of RAM and flash memory." Smart dust will forage subsist off power from its surroundings - e.g. smart dust near light will have a solar panel, while smart dust in high temperatures will convert heat into electricity.
Smart dust will primarily be used to monitor every movement of big structures like bridges or skyscrapers, or report on the environment inside a home - or even our bodies. It might be possible to run an internet search like "Where is my remote?"