Adjectives must always agree on definiteness with the noun they are modifying. Therefore, "The good teacher" is "المعلمة الجيدة", with both the noun and the adjective carrying the definite article. "المعلمة جيدة" can only mean "The teacher is good", because the adjective isn't carrying the definite article to show direct agreement with the noun.
On a slightly related note, another instance where the definite article changes the meaning and can be required is with the words "هذا" and "ذلك", and their other forms. When a noun follows one of these demonstratives and is indefinite, it is an X = Y sentence, e.g. "هذا طاولة جميلة", meaning "This is a pretty table". When a noun follows one of these demonstratives and is definite, however, the meaning is this X, e.g. "هذا الطاولة الجميلة غالية جدا", meaning "This pretty table is very expensive". Notice how the adjective directly modifying "table" – that is, "pretty" – has the definite article, and how the adjective following the copula in English is indefinite.
I hope this helped, I might have gotten a bit carried away!