The uniformity of the main magnetic field measured in ppm. In a defined volume it is the difference between maximum and minimum field strength and this multiplied by 1 million.
In MR, the homogeneity of the static magnetic field is an important criterion of the quality of the magnet. Homogeneity requirements for MR imaging are generally lower than the homogeneity requirements for NMR spectroscopy, but for most imaging techniques must be maintained over a large region.

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.

The field homogeneity is a very important factor for image quality. The field should be homogenous in the range of 1-10ppm over 30-50cm for high-quality imaging.

Quick Overview

A disturbance of the field homogeneity, because of magnetic material (inside or outside the patient), technical problems or scanning at the edge of the field.
When images were obtained in a progression from the center to the edge of the coil, the homogeneity of the field observed by the imaged volume, changes when the distance from the center of the volume increase. The same problem appears by scanning at a distance from the isocenter in left-right direction or too large field of view.
There are different types of bad image quality, the images are noisy, distorted or the fat suppression doesn't work because of badly set shim currents.
E.g. by using an IR sequence, changes in the T1 recovery rates of the tissues are involved. The inversion time at the center of the imaged volume is appropriate to suppress fat, but at the edge of the coil the same inversion time is sufficient to suppress water. Since the inversion time is not changed, the T1 recovery rates will increase.

Take a smaller imaging volume (and for fat suppression a volume shimming), take care that the imaged region is at the center of the coil and that no magnetic material is inside the imaging volume.

(FOV) Defined as the size of the two or three dimensional spatial encoding area of the image. Usually defined in units of mm². The FOV is the square image area that contains the object of interest to be measured. The smaller the FOV, the higher the resolution and the smaller the voxel size but the lower the measured signal. Useful for decreasing the scantime is a field of view different in the frequency and phase encoding directions (rectangular field of view - RFOV).
The magnetic field homogeneity decreases as more tissue is imaged (greater FOV). As a result the precessional frequencies change across the imaging volume. That can be a problem for fat suppression imaging. This fat is precessing at the expected frequency only in the center of the imaging volume. E.g. frequency specific fat saturation pulses become less effective when the field of view is increased. It is best to use smaller field of views when applying fat saturation pulses.

Smaller FOV required higher gradient strength and concludes low signal. Therefore you have to find a compromise between these factors. The right choice of the field of view is important for MR image quality. When utilizing small field of views and scanning at a distance from the isocenter (more problems with artifacts) it is obviously important to ensure that the region of interest is within the scanning volume.
A smaller FOV in one direction is available with the function rectangular field of view (RFOV).

See also Field Inhomogeneity Artifact.