Classification is important because it helps scientists to clearly identify species, study and observe them, and organize concentrated conservation efforts. It also assists as a way of remembering and differentiating the types of organisms, making predictions about organisms of the same type, classifying the relationship between different organisms, and providing precise names for organisms.
Although it seems strange and counter-intuitive, classifying organisms can be a reminder of some of their basic characteristics. It would be nearly impossible to remember all the details about a particular species without categorizing it with others that are similar. For example, if an animal is classified as a cat, immediately we already know that it has four legs, a tail, ears and whiskers, based on the way they are classified.
Knowing classifications also helps to predict the characteristics that a particular animal might have, based on the observation of others within the same classification. Still using the example of a cat - if someone has a house cat and has observed that the house cat can jump well, and they know that a tiger is also a cat, they might predict that tigers can jump well, even without knowing very much about tigers. Additionally, classification enables scientists to explain the relationships between organisms, which is helpful in trying to reconstruct the evolutionary roots of a particular species.
Finally, taxonomic names provide unique descriptive names for organisms. This is sometimes an issue with common names of animals. For example, there is a fish called a pickerel in Canada and in the US; however, one can be eaten and another cannot. This is because they are scientifically different species that both have the same common name. Scientific names give us more clarity on this issue than common names.