Botanical nomenclature?

http://en.wikipedia.org/wiki/Binomial_nomenclature
http://en.wikipedia.org/wiki/Botanical_nomenclature

What is Botanical name / Latin name?

http://en.wikipedia.org/wiki/Binary_name

What is Plant taxonomy?

What is Cultivar?

What is the meaning of "var." in some latin name we see?

http://en.wikipedia.org/wiki/Variety_(biology)
In botanical nomenclature, variety is a low-level taxonomic rank below that of species: As such, it gets a ternary name (a name in three parts).

A variety will have an appearance distinct from other varieties, but will hybridize freely with those other varieties (if brought into contact). Usually varieties will be geographically separate from each other.

Example: The pincushion cactus, Escobaria vivipara (Nutt.) Buxb., is a wide-ranging variable species occurring from Canada to Mexico, and found throughout New Mexico below about 2600 m. Nine varieties have been described. Where the varieties of the pincushion cactus meet, they intergrade. The variety Escobaria vivipara var. arizonica is from Arizona, while Escobaria vivipara var. neo-mexicana is from New Mexico.

Notes: To plant breeders, at least in countries that are signatory to the UPOV Convention, "variety" or "plant variety" is a legal term. In zoological nomenclature, the only officially-regulated rank below that of species is that of subspecies. Forms and morphs are used instead of varieties if needed, but are unregulated by the ICZN. In bacteriological nomenclature "variety" and "subspecies" are used interchangeably.

What is the meaning of "cf." in some latin name we see?

cf. is an abbreviation for the Latin derived (but also modern English) word confer, meaning "compare" or "consult". It is mainly used in common and statute law contexts as well as in academic writing.

Thus "cf." is often used by authors in the text of their article or book to refer to other academic material which may provide auxiliary information or arguments to the understanding of theirs.

It is sometimes used (primarily in dictionaries) to imply insight into the preceding word's etymology — that is, to suggest how one term obtained its particular naming convention (perhaps from another phrase). For example, the phrase "Big Whack (cf. Big Bang)" suggests to the reader that the usage of the moniker (self given nickname) Big Whack derives at least its name from the latter.

In the system of binomial nomenclature, the use of "cf." is similarly used to indicate that the species need be seen in context of its comparison to another, but by definition is not confirmed as the same. For example Corvus cf. splendens indicates "a bird similar to the House Crow but not certainly identified as this species". For this reason many mistakenly believe that "cf" is an abbreviated form of "confirmed" or "inconfirmatus" or the like.