Each biological system is based on the species as most important systematic character. A species first is a group of all individuals different from other groups in important characters. In contrary members of a species have equally important characters in common, as they do not with other groups.
Systematic groups in modern biology also are referred to as a taxon, taxa in the plural. Modern systematics therefore also is called taxonomy.
When the term "species" was introduced in biology, the characters used in telling species apart from each other, were exclusively morphological characters that you could see. Therefore the scientific word "species" comes from the Latin word "specio" - "I see".
But here are several examples for organisms looking very different, but still belonging to one and the same species:
A biological species is not only a morphological unit of similar organisms, but also a population of potential mating partners and so last, but not least, a genetic unit. A biological species, as of today, is the group of all organisms, that can potentially procreate offspring over several generations. Potentially, because mating is possible, but may not happen. Over several generations, because related species may procreate bastard offspring, but it will be sterile (an example is the mule from horse and donkey).
According to Mayr (1967), species are "groups of actually or potentially reproducing populations, that are reproductively isolated from other groups."
If the isolation of partial groups of a species should be so far, that apart from geographical isolation there is also reproductive isolation (for example because of adaptation to different ecological habitats), the species will divide and new species will develop, which is called speciation. The reproductive isolation need not expressively happen, because copulation is anatomically impossible: It may also happen precygotically (before fertilisation) or postcygotically (after fertilisation).
Due to reproductive isolation from other groups, species are genetic units. The collective genetic information of a species is called their gene pool. The isolated inheritance of species specific characters also leads to their conservation (if they indeed are inherited), and so the gene pool is also an information storage. Together with the genetic unity of the species there usually also is an optimal adaptation of the species to a specific ecological niche. Apart from being a genetic unit, a species also is an evolutive and an ecological unit.
The reproductive species definition also is not able to explain all of the variability of biological species. Except the already described conditions, there may be bastards between closely related species, in all other regards sufficiently special to be called a species. This happens in the plant kingdom, for example, referred to as allopolyploidy, but also in the animal kingdom, for example in many terrestrial snail groups. Species bastardization makes it necessary, to return, to some extent, to the morphological definition of species.
The conditions are similar in mainly parthenogenetic species or organisms reproducing asexually (so called agamospecies). Here the reproductive isolation is not entirely applicable. In the same way, the reproductive isolation of fossil species can often not be retraced. In that case, morphological characters must be used to determine if reproductive isolation may potentially have existed.