Us scientist don't actully call classification "clalssification", we call it Taxonomy because that Is the type/method of classification that we use. It basically means to "name things".
The system that other scientist as well as me use (taxonomy) was created by Carolus Linnaeus. Where a level of organiztion/clasification is called eather a Taxon or a taxonomic category. Carolus was born in 1707 but now rests in peace since 1778.
In taxonomy there are many key words to know such as: Genus, Species, Family, Order, Class, Phylum and kingdom.
Species are groups of close-related organisms that can interbreed. An example of this are dogs, which are closely related and can create offsprings between them.
Genus is a group that has really closely related species and it goes over species but under family. An Example is Rosa which has over 100 types/species of roses.
Family goes between Genus and Order. It is a group of one or more genera that have lots of characteristics in common. An Example is "Felidae", (cats).
Order is the name of a group that consist of similar families. An example is "carnivoria" which are large omnivores and carnivores.
Class is a group that consist of similar Orders. An example is "Mamamlia" Which are mammals.
Kingdom is the largest Taxom, it consist of similar phylia. An Exampe of it is "Animalia" (animals).