Definitions of grammar
We use the term grammar to encompass everything that we are told to "check" when we write. This checking process, however, covers different components that are not included in the specific definition of "grammar."
Attitude toward grammar
One way to improve your skills as editors of the elements broadly included under grammar, you should try to develop a habit of paying attention to what you see happening in the language around you. If you study the rules of grammar and then check out how they are or aren't being followed in ads, songs, publications, conversations, etc., you will begin to develop a context for these grammar rules and be able to apply them correctly in your own writing.