One of string theory's greatest achievements is the calculation of the black hole entropy from a microscopic point of view.
Entropy is a measure of how many ways you can re-arrange the microstates of a particular macrostate without changing its overall macroscopic form. More precisely, you take the logarithm of that number, w, and and then multiply it by Boltzmann's constant, k. So, the formula for entropy in statistical mechanics is given by S = k \space log \space w Note that S is entropy, as 'E' is already used for energy. However, this calculation requires a knowledge of atoms. But, since the atomic hypothesis wasn't formed until the late 19th century, the old way of calculating entropy was purely thermodynamical, involving the temperature of the object. Boltzmann's use of statistical mechanics in calculating entropy revealed what it 'really' was.
So, now to black holes. Jacob Bekenstein proposed that black holes entropy proportional to the size of their event horizons. However, he was met with opposition due to the fact that anything that has entropy needs to have a temperature, and there didn't seem like any way a black hole could emit radiation. However, Stephan Hawking showed that black holes will emit Hawking Radiation. So, the equation they derived for the entropy of a black hole is S_BH = \frac {kA} {4l_p ^2}
Where l_p is the Planck length, and A is the area of the event horizon. Note that like the original calculation of entropy, this is purely thermodynamical - it makes no mention of microstates. So, since any theory of quantum gravity describes spacetime over very short distances, it is a litmus test of a theory of QG to derive a microscopic formula for black hole entropy.
This was done in string theory by Cumrun Vafa and Andrew Strominger. In M-theory, along with one dimensional strings, multi-dimensional branes are used. So, you can treat a black hole as a black P-brane. The type of black hole that was used was a BPS black hole, a black hole with both mass and charge. Or, a BPS black P-brane. Vafa and Strominger showed that because of unbroken supersymmetry near the black hole, if we allow the charge to be small, then this black p-brane can actually be described by a group of D-branes. And calculating the entropy of this system of D-branes ends up giving the same result calculated thermodynamically by Hawking.
