There are plenty of reasons that led to the development of applied linguistics as a science. There are also reasons today that grant that the expansion of this field continues as extensively as possible.
The study of applied linguistics is a product of the growing interest in international languages that surfaced during the 1950s. This boom in interest came as a result of the launching of the Sputnik, which cemented the solidity of Russia as a world power that. At that point, Russia had not only rivaled, but now seemed to have surpassed, the United States. The essential question that was asked then was: are we equipped to make international citizens out of Americans or are we only good enough in our own turf. This is what propitiated the need to revise the teaching of English as a universal language, and it also prompted the motivation to teach *and understand* other languages.
It is important to realize that the job of the linguist is not to try and speak as many languages as possible. That is what polyglots and translators may aim to do. The linguist uses the scientific method to break down language as a system, and then understand its origin, the trends in usage, and the society that uses it. Speaking a language without taking the time to at least understand the origin of the words that we use everyday is doing a disservice to our own ancestry.
In the 21st century, linguists are quite busy determining patterns in the language and processing of information that happens in computers. Computational linguistics is the study of the statistical modeling of natural language as it is applied to technology applications. As you can see, it is the same concept as with the study of applied linguistics: to observe the patterns, rules, and usage of a system of communication. It is imperative to understand trends and patterns in order to predict what will happen, or may happen, next.
Hence, the field of linguistics and all of its sub-fields are essential to the study of human behavior, origins, social interaction, history, and even science.