Zoelula provided an excellent explanation.
One thing to add is that ketones are readily noticeable because of a distinctive "fruity" odor in the urine.
Ketones are a byproduct from the use of fat as fuel. Fat breakdown increases as less glucose becomes available due to a lack of insulin. When someone's urine or blood shows large amounts of ketones, this can lead to Diabetic Ketoacidosis or DKA. This is a life-threatening emergency which occurs when blood sugars have been consistenly over 300. This occurs more commonly in Type 1's, often at diagnosis, but can also occur in Type 2's who have been diagnosed long enough that they don't produce much insulin or the insulin production is overwhelmed by serious infection or stress. If someone's blood sugar has been in this range for awhile and they start experiencing flu like symptoms or vomiting they should go to the ER.