Do you remember the first day of Japanese class or the first day you resolved to finally learn the language on your own? What about the very first Japanese words you ever learned? There's a good chance arigatō gozaimasu (ありがとうございます) were those first words and/or you learned them on that first day of study. Of course the Japanese words for "thank you" are so widely known that you may not even have needed to "learn" them — they might have been something you were already aware of.
Unfortunately, however, many students' ability to express their appreciation never expands beyond this single phrase. Learning how to diversify the ways of saying "thanks" will allow you to be appreciative more naturally in many different situations.
Sure, we can attach the all-purpose adverb dōmo (どうも; to a great extent) to the front to give us dōmo arigatō gozaimasu (どうもありがとうございま; thank you very much), thereby drawing out the number of syllables and, thus, the level of politeness just slightly, and dōmo arigatō alone is serviceable in more casual situations. But these variations don't really give us anything beyond what we already know.