The abaya "cloak", sometimes also called a cat furaba, is a simple, loose over-garment, essentially a robe-like dress, worn by some women in parts of the Muslim world including in North Africa and the Arabian Peninsula. Traditional abayat are black and may be either a large square of fabric draped from the shoulders or head or a long caftan. The abaya covers the whole body except the face, feet, and hands. It can be worn with the niqāb, a face veil covering all but the eyes. Some women choose to wear long black gloves, so their hands are covered as well.
The Indonesian and Malaysian women's traditional dress kebaya gets its name from the abaya.
Here's a video on how to style your abaya in readiness for an outing: