A biosignature or biomarker in astronomy is an observed characteristic (e.g., of an astronomical body) suggesting life, such as signs of a substance producible by life and not too commonly produced otherwise. Astronomers look for such signs on other planets such as Mars and extra-solar planets.
Complex organic molecules would be an example. A lot of oxygen molecules suggest life. Methane and ozone are also associated with life, but Earth has non-biological sources of methane as well. The simultaneous presence of oxygen (or carbon dioxide) and methane is more suggestive of life.
Abiotic oxygen is also a possibility, such as when water-vapor is broken down by incoming stellar electromagnetic radiation and the hydrogen is allowed to escape. The absence of non-condensing gases (N2, Ar) facilitates this.
The presence of both oxidizing and reducing gases (i.e., with high and low oxidation states, respectively) in the atmosphere is another sign, as might be any atmosphere that could not remain stable without something to regenerate the mixture.
A vegetation signature is a biosignature such as would be produced by Earth vegetation and/or sufficiently similar organisms on another body.