Combination of 'trashy' and 'shaggy', usually used to describe one's hair but can be used to describe one's general appearance as well.
Traggy hair is not bed-head hair or blown-in-the wind hair, it's uncooperative hair. Despite your best efforts to make it look good, it just hangs out of style and looks poorly groomed.
Whoa, my hair is traggy today - what was my effort worth? I could have just just run my fingers through my hair after getting out of bed or just come in from the wind.