What Exactly Is Grammar?

The dictionary defines grammar as "the study or rules of a language's inflections or other means of showing the relations between words." This might sound obscure but is quite helpful; grammar is about relationships.
Imagine you have a heap of cards with single words on them: I, bake, cake, enjoy, afternoon. You could convey a message with them, but it would be clumsy and very inexact. Compare the fully inflected sentence: "I enjoy baking cakes in the afternoon." The combinations, connections, plural forms etc, make the sentence clear; all this is grammar.
You might think you "don't know any grammar" if you didn't study it much at school; but everybody knows grammar even if they haven't learned the technical terms. In fact, some linguists believe that the ability to learn grammar rules is part of the human brain; which is why, to a great extent, we do pick up the main rules of our language without being taught.