(ppm) A unit of proportion equal to 10^-6.

Chemical shift depends on the nucleus and its environment and is defined as nuclear shielding / applied magnetic field. Nuclei are shielded by a small magnetic field caused by circulating electrons, termed nuclear shielding. The strength of the shield depends on the different molecular environment in that the nucleus is embedded. Nuclear shielding is the difference between the magnetic field at the nucleus and the applied magnetic field.
Chemical shift is measured in parts per million (ppm) of the resonance frequency relative to another or a standard resonance frequency.
The major part of the MR signal comes from hydrogen protons; lipid protons contribute a minor part. The chemical shift between water and fat nuclei is about 3.5 ppm (~220 Hz; 1.5T). Through this difference in resonance frequency between water and fat protons at the same location, a misregistration (dislocation) by the Fourier Transformation take place, when converting MR signals from frequency to spatial domain. This effect is called chemical shift artifact or chemical shift misregistration artifact.

Inhomogeneity is the degree of lack of homogeneity, for example the fractional deviation of the local magnetic field from the average value of the field. Inhomogeneities of the static magnetic field, produced by the scanner as well as by object susceptibility, is unavoidable in MRI. The large value of gyromagnetic coefficient causes a significant frequency shift even for few parts per million field inhomogeneity, which in turn causes distortions in both geometry and intensity of the MR images.
Manufacturers try to make the magnetic field as homogeneous as possible, especially at the core of the scanner. Even with an ideal magnet, a little inhomogeneity is always left and is caused in addition by the susceptibility of the imaging object. The geometrical distortion (displacement of the pixel locations) are important e.g., for some cases as stereotactic surgery. Displacements up to 3 to 5 mm have been reported. The second problem is the undesired changes in the intensity or brightness of pixels, which may cause problems in determining different tissues and reduce the maximum achievable image resolution.

General strategies for reducing field inhomogeneity induced artifacts:
Increasing the strength of the gradient magnetic field.
Decreasing the echo time.
Improving the image resolution. Phase encoding. Postprocessing.

When a group of spins is placed in a magnetic field, each spin aligns in one of the two possible orientations. The relative numbers of spins with different alignments will be given by the Boltzmann distribution.
Definition: if a system of particles, which are able to exchange energy in collisions is in thermal equilibrium, then the relative number (population) of particles, N1 and N2, in two particular energy levels with corresponding energies, E1 and E2, is given by N1/N2 = exp [-(E1 - E2)/kT] where k is the Boltzmann constant and T is the absolute temperature.
For example, in NMR of protons at room temperature in a magnetic field of 0.25 tesla, the difference in relative numbers of spins aligned with the magnetic field and against the field is about one part in a million; the small excess of nuclei in the lower energy state is the basis of the net magnetization and the resonance phenomenon.