Trouble understanding the Bohr model of the atom

You are missing nothing. The Bohr model of the atom is false, and nowadays we replace the idea of the semi-classical "orbit" of Bohr with the fully quantum mechanical notion of orbitals or electron clouds, which give a probability distribution for the position of the electron around the nucleus, but do emphatically not imply that the electron is moving in any classical sense.

The reason the Bohr model was conceived of is that it can explain spectral emission/absorption lines like the Rydberg series by the energy difference between the orbits without being a full quantum theory, and it hails from a time when we did not yet understand quantum mechanics. Though its classical picture of orbits is completely false, its predictions for their energy levels are (modulo more subtle quantum effects) correct. Since, at the time, it was the first model to somewhat successfully explain the spectral lines, it has stayed around.

The following passage has been extracted from Bohr's Nobel lecture:

While in contradiction to the classical electromagnetic theory no radiation takes place from the atom in the stationary states themselves, a process of transition between stationary states can be accompanied by the emission of electromagnetic radiation, which will have the same properties as that which would be sent out according to the classical theory from an electrified particle executing an harmonic vibration with constant frequency.

Bohr proposed this as an postulate (premise or starting point of reasoning). So, in a sense, he said this as a definition.