Each world has a tech level that represents the technological sophistication of the world's society. It roughly corresponds, not to the level of technology known to the world, but to the level of technology that is widely available to the population. In addition, the empire knows about individual technologies such as starship technology or ambrosia technology. Technologies roughly correspond to the knowledge to create a ship, material, or device.
Each technology requires a certain tech level. For example, the technology to build hunter-killers requires the bio-tech tech level. Each empire, however, must acquire each technology individually. For example, an empire whose capital has just reached the bio-tech level cannot automatically build hunter-killers. The technology to build hunter-killers must be discovered by the research scientists of the empire. Once an empire has developed all the technologies for a given tech level, the capital is able to advance to the next tech level.
Once an empire has acquired the technology to build a resource, any world of sufficient tech level is able to build the resource. For example, once an empire has discovered hunter-killer technology, all bio-tech level worlds will be able to produce hunter-killers. More primitive worlds, however, will not.
Worlds other than the capital will increase in tech level to match the technology of the capital. An increase in tech level will happen roughly every four or five years on average. Note that any world that has a greater tech level than the capital will regress in tech level at the same rate until it matches the capital.
The capital, university worlds, and ruins worlds have a chance each year to discover new technology. The more university worlds and ruins worlds that the empire has, the greater the chance of discovering new technology. Once the empire has developed all the technology available to a tech level, a similar chance applies for advancing to the next tech level.