A type specimen is an example of an organism or thing that is the ultimate defining example for its category. Any time a scientist creates a scientific name - which means he or she has identified a species, genus, family, or some other taxonomic group that is distinct from all other related groups - that scientist must also choose a type specimen. The type should contain all the distinguishing characteristics of its taxon so it can serve as a reference and comparison for other scientists.
Except that's not strictly true. Really types have most to do with nomenclature - you can't have a valid scientific name without at least one actual object that holds that name.
Naming types is governed by strict rules. The International Commission on Zoological Nomenclature sets rules for naming animal types. An animal type can be an animal, a part of an animal, the work of an animal (fossilized footprints, wasps' nests if built before 1931), a colony, or a microscope slide. A photograph CANNOT serve as a type. Bacteria have their own nomenclatural code, which used to include rules for fungi. Fungi are now part of the exciting International Code of Nomenclature for algae, fungi, and plants. Obviously, so are plants.
I can only imagine how much fun it must be to attend the meetings that arrive at these codes.
The International Code gives use rules for typification. These rules are ... complex.
The different types of types are especially complicated. The most basic include:
1. Holotype, which is the main type designated by the author of the name.
2. Isotype, which is a duplicate of a type. Say, the author collects two specimens on the same day at the same place and designates the best one as the holotype - the other one can be an isotype.
3. Lectotype, a specimen - or illustration - created at the time that the name was created if the author didn't name a holotype at that time.
4. Neotype, a type chosen after the fact if there is no holotype or other original material.
5. Epitype, a type chosen to clarify an ambiguous holotype or lectotype.
There are others.
To designate plant types, botanists publish descriptions in the journal Taxon, which specializes in this field. Before Taxon was founded in 1951, botanists published these descriptions ... well, I don't really know. This is an area of plant taxonomy that I have always found opaque. How is it that botanists can keep track of these things, the designations of names and specimens and changes? Where do these types live? Anywhere? If so, how does anyone get to see them?
The Index Kewensis has kept up with nomenclature since 1885. This work continues with the International Plant Names Index (IPNI), which is trying to eliminate the need to consult umpteen primary sources. The Linnaean Plant Name Typification Project has been finding and digitizing the type specimens Linnaeus used for his names. Even so, botanical nomenclature and typification seems to assume a vast amount of pre-existing knowledge, and an inordinate attention to botanists, some of whom are so well-known they go by obscure abbreviations. If you don't already know the prevailing practices in this field, it's fairly hard to figure them out on your own. And it's very easy to get stuff wrong.
It's almost like practicing law.