In an age when the truth and inherent nature of everything is routinely questioned, it should come as no surprise that grammar education has come to be regarded as unnecessary and even pernicious. Teachers advocate integrated approaches in what are essentially programs designed to facilitate language learning by osmosis—students will "pick up" the rules of English by reading and writing on their own much better than when they are subjected to rote memorization of the parts of speech and the drudgery of sentence diagramming.
This view is about 100 years old....and the one that preceded it stretched from roughly the 8th century B.C. in Greece to the early part of the 20th century across the whole Western world. While length of tradition is no argument in itself, the fact that so many great intellectuals were the product of the direct approach to grammar instruction (and the fact that so few of similar ability remain) should count for something. Grammar formed the basis on which the rest of one's education was built—the "grammar stage" of Classical education was just that, a solid grounding in the nature and usage of language intended to facilitate literacy, critical thinking and the ability to form ideas from existing facts.
It's hard to find a good definition of grammar, largely because its importance has been questioned and its content ignored for so long. Currently it's most often described as the rules regulating language, but this is only part of the story. Grammar is the system of usage employed for a language to facilitate and codify meaning. In simpler terms, grammar is rules that do regulate language for the explicit purpose of aiding universal understanding among speakers of that language. If such linguistic governance does not exist, people who ostensibly speak the same language will not understand each other.
A commonly identified problem among those educated in the United States is that they retain a certain form of illiteracy from their earliest years through high school and even college. They can identify and even read words, but they cannot interpret them in any meaningful way and they certainly cannot form complex ideas or thoughts based on what they read. There are (as with anything) a variety of contributing factors, but one of the most basic is the lack of direct grammar education they receive.
To design a bridge one must first be fluent in the laws of physics and mathematics employed in such an undertaking. The same principle applies to language—in order to understand what sentences, paragraphs and books mean, a student must first understand why words are arranged as they are, why punctuation works the way it does, what different kinds of words exist and why they must change form depending on context, even what context itself is. Grammar is that study, and it is not simply an end in itself, it is the foundation for the very thing toward which education aims: comprehension.