A genus is a group of similar species in the biological classification. Grouping creatures in a scientific way is a kind of taxonomy. When scientists talk about one genus of animals or plants, they mean several species of those animals or plants that are closely related to each other.
The plural is different from other English words because it comes from Latin. Genus is the singular for only one group, and genera is the plural form of the word for two or more groups. Several genera make up a family.
When writing a scientific name of an organism, you write the name in italic, with the genus in front. For example, "Felis silvestris catus", Felis is the genus. The genus always begins with a capital letter.
As a common word [change]
To aid in the flow of words, genus names in Latin can be 'anglicised' to form a common name. For example, the genus Pseudomonas is "pseudomonad" (plural: "pseudomonads"). In practice, most really common animals and plants already have a common name. So instead of saying 'felids', or 'felines', one says 'cats'. The word 'cat' is used both for the family pet, and also as a general term for all the cat family (Felidae).