If you're kempt, you're neat and well-groomed. Your always-kempt house will be harder to keep tidy after you adopt six furry puppies.
In the U.S., it's much more common to see the word unkempt than kempt, but it's clear the two have opposite meanings. Your unkempt, scraggly beard might contrast, for example, with your brother's closely shaven, kempt face. The unkempt bedroom your sister is happy to inhabit is much messier than your own orderly, uncluttered, kempt room. Kempt shares a root with comb, which explains why it usually describes someone's tidy hair.