The theory of gravity in $3+1$ dimensions famously has black hole solutions, being the limiting configuration of a point mass gravitational source. In higher dimensional gravity, and in particular in higher dimensional supergravity, there are analogous solutions, which however are limiting configurations of a gravitational source that is supported on a line, or a surface, or a higher dimensional space. For a surface one might speak of black membrane solutions hence generally of black brane solutions.

The idea is that both these brane-phenomena are aspects of one single entity:

At low string coupling the D-brane/NS-brane description is accurate. Low string coupling implies that the coupling of gravity is weak, hence that the back-reaction of the branes on the background geometry is negligible.

At large string coupling but low energy, the effectivesupergravity description becomes accurate. Here the branes do back-react on the gravitational background and hence create the black brane spacetime geometry.

This duality of the brane picture is at the heart of the AdS/CFT correspondence. See there for more details.