The total number of independent data samples in the frequency and phase directions (number of pixels in the frequency encoding - and phase encoding direction).

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

Aliasing is an artifact that occurs in MR images when the scanned body part is larger than field of view (FOV). As a consequence of the acquired k-space frequencies not being sampled densely enough, whereby portions of the object outside of the desired FOV get mapped to an incorrect location inside the FOV. The cyclical property of the Fourier transform fills the missing data of the right side with data from behind the FOV of the left side and vice versa. This is caused by a too small number of samples acquired in, e.g. the frequency encoding direction, therefore the spectrums will overlap, resulting in a replication of the object in the x direction.
Aliasing in the frequency direction can be eliminated by twice as fast sampling of the signal or by applying frequency specific filters to the received signal.
A similar problem occurs in the phase encoding direction, where the phases of signal-bearing tissues outside of the FOV in the y-direction are a replication of the phases that are encoded within the FOV. Phase encoding gradients are scaled for the field of view only, therefore tissues outside the FOV do not get properly phase encoded relative to their actual position and 'wraps' into the opposite side of the image.

Use a larger FOV, RFOV or 3D Volume, apply presaturation pulses to the undesired tissue, adjust the position of the FOV, or select a small coil which will only receive signal from objects inside or near the coil. The number of phase encoding steps must be increased in phase direction, unfortunately resulting in longer scan times.
When this is not possible it can be corrected by oversampling the data. Aliasing is eliminated by Oversampling in frequency direction. No Phase Wrap (Foldover Suppression) options typically correct the phase encoding by doubling the field of view, doubling the number of phase encodes (to keep resolution constant) and halving the number of averages (to keep scan time constant) then discarding the additional data and processing the image within the desired field of view (but this is more time consuming).
Tissue outside this doubled area can be folded nevertheless into the image as phase wrap. In this case combine more than 2 number of excitations / number of signal averages with foldover suppression.
See also Aliasing, Foldover Suppression, Oversampling, and Artifact Reduction - Aliasing.

(bFFE) A FFE sequence using a balanced gradient waveform. A balanced sequence starts out with a RF pulse of 90° or less and the spins in the steady state. Before the next TR in the slice phase and frequency encoding, gradients are balanced so their net value is zero. Now the spins are prepared to accept the next RF pulse, and their corresponding signal can become part of the new transverse magnetization. Since the balanced gradients maintain the transverse and longitudinal magnetization, the result is, that both T1 and T2 contrast are represented in the image. This pulse sequence produces images with increased signal from fluid, along with retaining T1 weighted tissue contrast. Because this form of sequence is extremely dependent on field homogeneity, it is essential to run a shimming prior the acquisition. A fully balanced (refocused) sequence would yield higher signal, especially for tissues with long T2 relaxation times.

See Steady State Free Precession and Gradient Echo Sequence.

This family of sequences uses a balanced gradient waveform. This waveform will act on any stationary spin on resonance between 2 consecutive RF pulses and return it to the same phase it had before the gradients were applied. A balanced sequence starts out with a RF pulse of 90° or less and the spins in the steady state. Prior to the next TR in the slice encoding, the phase encoding and the frequency encoding direction, gradients are balanced so their net value is zero. Now the spins are prepared to accept the next RF pulse, and their corresponding signal can become part of the new transverse magnetization. If the balanced gradients maintain the longitudinal and transverse magnetization, the result is that both T1 and T2 contrast are represented in the image.
This pulse sequence produces images with increased signal from fluid (like T2 weighted sequences), along with retaining T1 weighted tissue contrast. Balanced sequences are particularly useful in cardiac MRI. Because this form of sequence is extremely dependent on field homogeneity, it is essential to run a shimming prior the acquisition.
Usually the gray and white matter contrast is poor, making this type of sequence unsuited for brain MRI. Modifications like ramping up and down the flip angles can increase signal to noise ratio and contrast of brain tissues (suggested under the name COSMIC - Coherent Oscillatory State acquisition for the Manipulation of Image Contrast).
These sequences include e.g. Balanced Fast Field Echo (bFFE), Balanced Turbo Field Echo (bTFE), Fast Imaging with Steady Precession (TrueFISP, sometimes short TRUFI), Completely Balanced Steady State (CBASS) and Balanced SARGE (BASG).

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

Black boundary artifacts are black lines following voxels where both water and fat protons are present in the same voxel. This artifact arise along the boundary of organs or tissues perpendicular to the frequency encoding direction, and occurs preferentially in gradient echo sequences with out of phase echo times.

Fat suppression techniques eliminate this artifact. For artifact reducing helps a smaller water fat shift (high bandwidth), a higher matrix or/and an in phase TE.

See also Chemical Shift Artifact.