@MissDaphne - That's really interesting! I studied Latin in school, so I'm more familiar with Latin principal parts and haven't really thought about them in English.
Latin teachers will often make their students memorize all the principal parts of a verb when they learn the vocabulary. (To use an English analogy, you wouldn't just say "write," you would say "write-writing-wrote-written.") That way, you don't just know what the verb means, but you know how to create all the forms of it and don't write the Latin equivalent of "writed."
It's also important to know the principal parts because it helps you recognize other forms of the verb. To use another English example, if you don't know that "wrote" is the past tense of "write," you could spend a lot of time looking it up in the dictionary!