Panspermia (or exogenesis) is the hypothesis that life on Earth originated from somewhere else in space, and that alien organisms arrived here on a meteor or something similar. The implication of the claim is that life is not unique to Earth, and that life on other planets will be chemically similar to terrestrial life.
While it is considered a "fringe" theory with few adherents, a small number of scientists are studying meteorite fragments, looking for signs of microscopic alien life.
This idea is actual fact in Star Trek. An ancient humanoid species seeded the galaxy with their DNA, including a coded message that would lead future humanoid races to learn about their "creators". The DNA was supposedly programmed to "evolve" a humanoid form on the various planets of the galaxy. Of course evolution depends on environmental conditions, and no alien can predict what a planet's environment will be like billions of years in the future. The episode only demonstrates that the TNG writers don't even begin to understand evolution.
A sort of reverse panspermia occurs in Stargate, in which aliens found humans to be extremely useful as laborers and host bodies. These aliens therefore captured humans from Earth to establish populations of humans on planets throughout the Milky Way galaxy and even in other galaxies.
- TNG "The Chase"