The Ethereal Plane is a misty and foggy dimension which overlaps with the The Prime Material Plane and the Inner Planes, meaning that every location on those planes has a corresponding location on the Ethereal Plane.
The Border Ethereal describes the areas of this plane which directly overlap one of the Inner Planes. From here, a creature can see through into the overlapped plane but the visions are misty and difficult to focus on.
The Deep Ethereal describes the areas of this plane which do not overlap with one of the Inner Planes. The mist and fog here is thick, reducing visibility, and coloured curtains drift around offering portals to the various Inner Planes.
Travel
Travel to The Ethereal Plane is achieved through various spells. In The Border Ethereal it's possible to travel to the plane that the current area overlaps with; in The Deep Ethereal, you must travel through a coloured curtain to reach The Border Ethereal which overlaps the corresponding plane.