This is a great question, and I think the reason you're getting different answers from your commenters is that the answer is in fact different in British English and American English. "Quite," "very," and "extremely" are all adverbs called intensifiers that change the degree of the adjective to which they're attached - but these words have different strengths in British and American English.
In American English:
very < quite < extremely
Here, "quite" is a little bit stronger than "very." It's not as commonly used in American English, but when it is, it often has a feeling of surprise: "This house is quite big! Bigger than I expected!"
In British English:
quite < very < extremely
Here, "quite" means something similar to "somewhat," and it's among the mildest intensifiers you can use: "This house is quite big, but I'm not sure it will fit all of us." In fact, sometimes it's so mild it can mean the opposite of what it seems! A statement like "The meal was quite nice," in certain situations, could be interpreted as "The meal was not actually nice, but I'm too polite to tell you what I really think."
Finally - just to be more confusing - in both British and American English, "quite" can sometimes mean "completely, 100%." For example, "I'm not quite finished" will always mean "I'm not 100% finished." This happens when the word "quite" is attached to a word that *can't* be intensified - in this example, you can either be "finished" or "not finished," and there are no degrees of judgment in between the two.