The scientific names for plants and animals comprise a name describing their type and start with a capital letter, followed by the name of the species in lower case letters, all written in italics. The species groups together all individuals capable of reproducing among themselves. Carl Von Linne (1707-1778) invented this categorization, which dates from the 18th. Century. It has the advantage of being written in Latin and is therefore independent of living languages.
With this name you may sometimes see a name in inverted commas which describes the variety or cultivar. The variety is a variant of the species which differs from the others by minor, stable characteristics. The variety is not natural - it is obtained from horticultural selection.
The types are grouped in families. These are based on resemblance, and on what is considered to be a common ancestor, in simpler form. These families are grouped in order, then in class, then in branches, and finally in a kingdom. This is a simplified version, as we also have intermediate branches and super-classes, sub-classes, etc...
By following these different levels of classification we can trace, by evolution, the living forms of ones compared to the others.
However, we still discover new species and researchers sometimes have to make modifications.
It's not always easy to remember the scientificname, so you mostly find the common or commercial name. But sometimes the common names used are wrong, as in the case of the geranium, which is really a palargonium (its scientific name), another plant entirely.
Take a first complete example, Man :
Common name : man
Kingdom : Animal
Branch : Vertebrates
Class : mammal
Order : Primates
Family : Hominidae
Type : Homo
Species : sapiens
Take another example, the tomato :
Common name : tomato
Family : Solanaceae
Type : Lycopersicon
Species : esculentum
Varieties : Marmande, Pyros, Roma, etc...
Some examples of families :
Begoniaceae : Begonia,...
Geraniaceae : Geranium, Pelargonium, ....
Orchidaceae : Cymbidium, Phalaenopsis,....