(Gφ) The phase encoding gradient is a magnetic field gradient that allows the encoding of the spatial signal location along a second dimension by different spin phases. The phase encoding gradient is applied after slice selection and excitation (before the frequency encoding gradient), orthogonally to the other two gradients. The spatial resolution is directly related to the number of phase encoding steps (gradients).

A technique, which produces a 3 dimensional image of an object. The advantage of this approach is that the signal, acquired from the entire volume has an increased SNR. 'Slices' are defined by a second phase encoded axis, which divides the volume into 'partitions'. There is no gap between the slices in 3D volume imaging, therefore thin slices are possible. The Gz phase encoding gradient is set for several slices in one. But 3D takes more time with thin slices because of this phase encoding gradient. With conventional thin slice imaging, the SNR is poor, with 3D volume imaging this is not the case because the slab (volume) is responsible for SNR.

Scanning of a volume instead of scanning single slices. The phase encoding gradient is used for two directions.

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.

(ASSET) ASSET is a parallel imaging technique of the SENSE type (image domain reconstruction).
Each coil element is sensitivity encoded and the covered spatial zone is mapped. By reducing the field of view in the phase encoding gradient direction the scan time decreases, but this images of each coil element contain foldover artifacts. The sensitivity profiles of the elements are used to calculate unfolded images.

See also Sensitivity Encoding, Generalized Autocalibrating Partially Parallel Acquisition.