Affinis is Latin for 'adjacent', and the root of the English word 'affinity'. The Latin word is still in use in the field of biology and taxonomy, where it is usually abbreviated to aff., and is sometimes found in the phrases n. sp., aff. or sp. nov., aff.* This indicates that a species is new and that the author doesn't want to firmly commit to a specific species name at this point, but notes that is looks a lot like this other species. The author is not making the claim that they may be the same species, only that they look as though they are probably related. The species name would be written something like this: Agenus aff. aspecies
Obviously, this is a temporary measure. If this state persists, we may refer to this name as a nomen dubium. Aff. may be applied to a genus in some cases, but will not be applied to higher taxonomic levels, as these are labeled as various forms of incertae sedis instead.
Aff. is sometimes confused with cf., however they are different in meaning; cf. indicates that the author believes that the new specimen may be a member of the known species, while aff. indicates that he believes that it is not a member of the known species.
*I am assuming that this stands for novum species affinis, but amazingly, I have been unable to confirm this.