How are the Four Noble Truths and the Eightfold Path important to Buddhists?
It could be said that The Four Noble Truths, and what they infer, are Buddhism itself. There are many traditions, schools, sects of Buddhism, but the Four Noble Truths are acknowledged in all of them, because they are foundational. They describe why Buddhism is needed, and what constitutes the essence of the practice of Buddhism. There may be various practices and ideas within Buddhism, but they are merely different expressions of the essence as expressed in the Four Noble Truths.