This family is known as the "Coffee" or "Madder" family and has 450 genera and around 6,500 species worldwide. These plants typically have simple leaves (undivided) that are opposite (two leaves at the node, usually near a lateral bud or shoot) or sometimes whorled (more than 2 around a node). Flowers usually have both male and female sex organs.
Genus: Coffea. Overall, the genus has about 100 species, only a few of which are commercially relevant.
Species: arabica makes up approximately 70% of the world's coffee production. Other species not so common in specialty include canephora (var."Robusta") and liberica. Of all of the Coffea species, only arabica is self-fertile, and therefore can be self-pollinated. The arabica species also typically have lower caffeine contents than canephora.
Image used with permission from Coffee Seed Physiology, Braz J. Plant Physiol., 18(1):149-163, 2006
What is a variety? Cultivar? Hybrid?
In the coffee industry we tend to use the below terms interchangeably despite the fact that they do have specific botanical meanings. For more in-depth geekery, visit http://apps.rhs.org.uk/rhsplantfinder/plantnaming/hownameswork.asp and http://www.kew.org/plants-fungi/Coffea-arabica.htm
Variety/Varietal: This rank of taxa delineates differences between plants that are smaller than in subspecies but larger than forms. A variety retains most of the characteristics of the species, but differs in some way.
Hybrid: Hybrids are created by crosses between two different species or two different forms of the same species. Hybrids may occur through naturally or selective breeding. For example, mundo novo is a hybrid of typica and bourbon. They are indicated in botanical terminology by a multiplication sign between the two parents.
Coffee - Tree or Shrub? Fruit or Tree?
Other growth information: Coffea has opposite leaves, which means the leaves branch out in matching pairs from the stem.
The fruit is a 2-seeded "drupe" fruit, commonly called the cherry. Technically a stone fruit, the seeds are the coffee "beans". However, if you squeeze open the coffee fruit you will find that there is hardly any "fruit" at all, but most of the drupe is filled by the two slippery seeds.
What is coffee skin? Parchment? Pulp?
The beans themselves are covered in the endocarp, known in the industry as parchment. Inside the parchment are the two coffee seeds, each covered by another membrane known as silver skin.