Space dust is really a cloud of gas in space. As individual gas particles get close together within these clouds, they begin to bump into each other. As they continuously come in contact, the gas particles begin to heat up. The cloud of gas then begins to contract as it heats up while gravity is simultaneously pulling on the particles within the cloud of gas. This creates an environment where the cloud of gas becomes stable and the particles are sort of stuck together like a ball. This ball of gas is extremely hot causing it to glow bright in the sky! These are all the bright dots we see in the sky as stars!

Space dust and gases collapse to form nebulae and then stars as a result of gravity. The above answer is a fairly good (if longer) description.