Niels Bohr introduced his model of atomic structure to explain certain phenomena that were noticed in the emission spectrum of atoms that could not be explained by theories that were in use to explain the structure of atoms.
Before Bohr came up with his theory the general view was that atoms have a nucleus made of protons and neutrons and the electrons in the atom orbited the nucleus like the planets orbit the Sun. The distance at which electrons could orbit from the nucleus or the orbital radius of the electrons could take on any value. If this were true, the emission spectrum of any atom would have consisted of a continuous range of frequencies.
It was not possible to explain the discrete frequencies of light in the emission spectrum of an atom with this theory. To explain that it was necessary to introduce the idea that electrons could exist only in a limited number of discrete energy levels each of which corresponded to a particular distance from the nucleus. This led Bohr to propose his model that introduced the concept that electrons can only exist in specific energy levels.
If you look at some of the other models at the time, none of them could account for two different findings that were important at the time Bohr's Model was conceived.
The first finding that led to the Rutherford model (central nucleus with orbitting electrons) was that the atom had a dense, positively charged nucleus with a cloud of electrons outside it.
However, just having random electron orbits didn't account for another finding at the time, where if you run electricity through a gas, you get a very specific set of light wavelengths emitted. For example, looking at the hydrogen spectrum (see link below), you see 4 wavelengths of visible light that are being emitted. If you believed Rutherford's model held true, then you would expect to see a bunch of light wavelengths depending on the electrons' energy.
Bohr refined Rutherford's model, saying that electrons could only orbit with certain energies, instead of any random energy. The differences between these energy levels lined up with the frequencies of light that were emitted, lining up this new model with experimental results.