The quantum mechanical structure of the atom says that electrons are not in definite orbits, but in probability densities called orbitals, which are much more messy.
The Bohr model sees the atom as a group of particles with definite positions and places, with electrons in nice, neat orbits around the nucleus in the center, moving progressively outwards. This is based on classical physics, and doesn't take into account our modern quantum physical knowledge.
Now we know, for instance, that tiny particles like electrons actually have an uncertainty in their position. This is called Heisenberg's Uncertainty Principle. Rather than being in one obvious location, electrons instead have a probability density, where they are most likely here, but could be there, and maybe even there. This is called an orbital.
We also know that orbitals make up the shells of electrons, and aren't nice neat circles at all, but complex and messy shapes, orientated along different axes in space. Orbitals with the same shape but angled differently are called subshells.
Quantum physics reveals to us a property of some particles called spin, and in electrons can be either
Fermi exclusion came about in quantum mechanics and says that no two electrons in an atom may have the same quantum numbers, which are unique properties and positions of each electron that explain to us a lot about how electrons and orbitals move and interact with each other.
Overall, we now view the atom as more messy, complex and uncertain than the Bohr model allows.