The frequency at which the resonance phenomenon occurs. The resonance frequency is given by the Larmor equation for MRI and is determined by the inductance and capacitance for RF circuits. An atom will only absorb external energy if that energy is delivered at precisely it's resonant frequency.
The Larmor equation states that the resonance frequency of a magnetic nucleus (the radio frequency needed to excite a nucleus to the higher spin rate) is directly proportional to the magnetic environment it experiences. Atoms such as hydrogen-1 (1H) and phosporous-31 (31P) resonate at different Larmor radio frequencies because of differences in the magnetic properties of their nuclei. The resonance frequency at 1.5 T for 31P is 25.85 MHz, for 1H, 63.86 MHz.

See also Larmor Frequency.

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.

(MR) Resonance phenomenon resulting in the absorption and/or emission of electromagnetic energy by nuclei (for that reason also nuclear magnetic resonance) or electrons in a static magnetic field, after excitation by a suitable RF magnetic field.
The peak resonance frequency is proportional to the magnetic field, and is given by the Larmor equation. Only unpaired electrons or nuclei with a spin exhibit magnetic resonance. The absorption or emission of energy by atomic nuclei in an external magnetic field after the application of RF excitation pulses using frequencies, which satisfy the conditions of the Larmor equation.
The magnetic resonance phenomenon may be used in one of these ways:
By manipulation of the external field (application of gradient fields), the resonance frequency can become dependent on spatial location, and hence images may be generated (MRI).
The effect of the electron cloud in any atom or molecule is to slightly shield the nucleus from the external field, thus giving any chemical species a characteristic frequency. This gives rise to 'spectra' where nuclei in a molecule give rise to specific signals, thus facilitating the detection of individual chemicals by means of their frequency spectra (MRS)

Quick Overview
Please note that there are different common names for this artifact.

During frequency encoding, fat protons precess slower than water protons in the same slice because of their magnetic shielding. Through the difference in resonance frequency between water and fat, protons at the same location are misregistrated (dislocated) by the Fourier transformation, when converting MRI signals from frequency to spatial domain. This chemical shift misregistration cause accentuation of any fat-water interfaces along the frequency axis and may be mistaken for pathology. Where fat and water are in the same location, this artifact can be seen as a bright or dark band at the edge of the anatomy.
Protons in fat and water molecules are separated by a chemical shift of about 3.5 ppm. The actual shift in Hertz (Hz) depends on the magnetic field strength of the magnet being used. Higher field strength increases the misregistration, while in contrast a higher gradient strength has a positive effect. For a 0.3 T system operating at 12.8 MHz the shift will be 44.8 Hz compared with a 223.6 Hz shift for a 1.5 T system operating at 63.9 MHz.

For artifact reduction helps a smaller water fat shift (higher bandwidth), a higher matrix, an in phase TE or a spin echo technique. Since the misregistration offset is present in the read out axis the patient may be rescanned with this axis parallel to the fat-water interface. Steeper gradient may be employed to reduce the chemical shift offset in mm. Another strategy is to employ specialized pulse sequences such as fat saturation or inversion recovery imaging. Fat suppression techniques eliminate chemical shift artifacts caused by the lack of fat signal.

See also Black Boundary Artifact and Magnetic Resonance Spectroscopy.

The interaction of the patient with the RF coil, which causes shifts of the resonance frequency and damping of the coil's resonance and hence reduction of the quality factor because of magnetic induction and dielectric losses in the patient.
The design and construction of a MRI coil is determined by the load on the coil. The load is either a phantom or the actual sample being imaged.

See also Radio Frequency Coil.