In lower dimension structure such as quantum wells. The wavefunction of the electron is confined so that it can only move freely in 2D. How does it lead to a larger band gap and greater absorption strength?
When a quantum particle is confined, its ground state energy increases — that's so called zero point energy. In semiconductors quantum particles are both electrons and holes. Since ground state of electrons goes up, and that of holes goes down — farther from band edge, effective band gap — difference between ground states of electron and hole — increases.
As for absorption strength, the electrons and holes are more localized in the quantum well, thus there's much higher overlap between electron and hole wavefunctions. Since this means that there's higher probability of finding both the electron and hole near the quantum well, probability of recombination increases. Absorption is the reverse of recombination, so its probability is also increased.