When you're abed, you're lying in your bed. You might be late for breakfast with your family because you lie abed long after your alarm goes off.
The word abed is very old fashioned, and you're most likely to come across it in a book. A character in a 19th century novel might lie abed all day before being diagnosed with scarlet fever, for example. Abed is rooted in the Old English on bedde, or "in bed, from the sense of a- meaning "on" — which is also found in words like "alive," "asleep," and "afoot" — and bed.