A type species is an individual specimen (either tangible, fossilized, or an illustration) that fixes the name of a genus (or of a taxon in a rank lower than genus). Two different definitions are used interchangeably, in a general term and a botanical term.
Strictly speaking, a type species exists only in zoological nomenclature. As set in article 42.3 of the International Code of Zoological Nomenclature, the type of the name of a genus or subgenus (a "genus-group name") is the "type species". This is defined as "The nominal species that is the name-bearing type of a nominal genus or subgenus". The species name in turn is fixed to a type specimen.
In botanical nomenclature, the type of a name of a genus or species is a specimen (or illustration) (ICBN, articles 10.1, 8.1 and 10.4). This type will usually be the type of an included species, in which case it can be indicated by the name of this species (Art 10.1). This species is called the "type species", but this phrase has no formal standing. The botanical type specimen itself is generally called a "type specimen."