Grammatical means following the rules of how words are properly arranged and used in a language. When a sentence is grammatical, it's built correctly according to the patterns that make a language work. “The dog chased the ball” is grammatical. “Dog the ball chased the” uses the same words but isn't grammatical because English doesn't arrange words that way.

Every language has grammar: rules about word order, verb forms, plurals, and how sentences fit together. These rules aren't arbitrary. They're patterns that developed so people could understand each other clearly. When you learn that verbs need to match their subjects (“she runs” not “she run”), you're learning grammar.

Something can be grammatical without being particularly good writing. “The very large dog chased the round ball quickly” is grammatical but clunky. Good writing requires both grammatical correctness and style.

The opposite is ungrammatical or not grammatical. Native speakers usually know what sounds grammatical without thinking about it, though they might not be able to explain why. That's because you absorbed your language's grammar by hearing it thousands of times before you ever studied it in school. When you study grammar formally, you're learning to understand rules you already use instinctively.