What is Abaft the beam?

"Beam" refers to a measurement of the width of a ship. The width at the widest points of a ship can be measured as a beam. "Abaft" indicates the direction of being behind or towards the rear. In the context of ship structure, that is the stern of the ship, the very back of it.  

The term "Abaft the Beam" means the bearing or direction between the beam of a ship and the stern of it.

This term is often applied to identifying the situation of ship/vessel overtaking. Overtaking another vessel means that the first vessel has to get approached the stern of the second one, pass by on either side, and then keep moving forward. To be specific, Vessel A should be considered as overtaking Vessel B when Vessel A comes from a direction of more than 22.5 degrees abaft Vessel B's beam.

Any vessel overtaking any other should keep out of the way of the vessel being overtaken. The former is the give-way vessel, and the latter is the stand-on vessel.