People have been studying the natural environment since the days of Aristotle and we have learned much about organisms by watching, dissecting and studying them. Humans have a natural tendency to organise and put things into groups, this includes the natural environment and the organisms around us.
We have developed several systems in order to understand the relationships between organisms and also to allow us to clearly talk about the same species! In some cases, scientists have been studying a species for years only to find out that they were looking at two distinct organisms! Classification allows us to avoid this confusion and allow the gradual progression of science to add to the bank of knowledge about our world.
The distinction between two species can be as small as a slight difference in the noise they make. Species of birds have been officially identified this way after computers and software have enabled close analysis of bird calls and scientists have been able to distinguish between two species. These investigations can later be followed up with genetic analysis which can conclusively demonstrate the differences between species.
Remember that evolution drives species towards developing new adaptions, suited to the biotic and abiotic conditions that they experience. These changes can be large or small, from growing wings to slight changes in cell structure and function. Our efforts to classify these changes help us paint a big picture view of evolutionary changes and speciation over time.