Someone who's frowsy looks like a slob. If you go to a job interview looking frowsy, you're less likely to get the job than if you comb your hair and wear a tidy suit.
If you sleep in your clothes so that you can roll out of bed in the morning and walk right out the door to catch a bus for school, you're in danger of looking frowsy. Frowsy people are untidy and scruffy — sometimes even dirty, with unwashed hair and grubby fingernails. Frowsy and its variation frowzy probably come from the now-obsolete adjective frowsty, "having an unpleasant smell."