In the context of relativity, “observer” can mean two different things.
Often, observer is synonymous with reference frame or (spacetime-)coordinate system: An observer in this sense is someone who assigns coordinate to everything that happens around him. In particular, all events are assigned space coordinate values and a time cordinate value. In the context of special relativity, it is often the case that when there is talk of an observer, what is meant is really an inertial observer, corresponding to a special type of reference frame.
On other occasions, the term is used in a more narrow sense – in those cases, an observer is someone sitting at a certain point in space and using the light signals reaching that location to construct an image of his surroundings. In the context of optical effects in relativity, for instance gravitational lensing, observer is usually meant in this way.