Diabetes causes high blood sugar which can damage the blood vessels that lead to your nerves. This can cause nerves to lose their ability to feel sensation. This problem is called neuropathy. While not feeling doesn't sound like a huge problem, it can mean the difference between losing a foot or not.
People with normal sensation will feel if their shoe is rubbing on a toe or certain part of their foot and correct the problem with either taking off the shoe, or re-tying the laces to give more room. People with neuropathy don't feel the rubbing and often take off their shoes to find a bloody mess of a shoe rubbing on their foot all day. The same goes if there is a rock, pebble or sharp edge in a shoe, without feeling pain, you don't know if something is irritating your foot.