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

Backfolding always occurs due to wrong phase encoding caused by objects outside the planned FOV. Phase encoding gradients are scaled for the field of view only. Tissues outside the FOV do not get properly phase encoded relative to their actual position and 'wraps' into the opposite side of the image. The Backfolding artifact projects image contents which fall outside the imaging FOV back into the image; the back folded information thus reappearing on the other side of the image. In fact, information along the phase encoding direction can be viewed as projected onto a cylindrical screen with a circumference corresponding to the linear field of view dimension in the phase encoding direction.

See also Aliasing Artifact.

(BW) Bandwidth is a measure of frequency range, the range between the highest and lowest frequency allowed in the signal. For analog signals, which can be mathematically viewed as a function of time, bandwidth is the width, measured in Hertz of a frequency range in which the signal's Fourier transform is nonzero.

A higher bandwidth is used for the reduction of chemical shift artifacts (lower bandwidth - more chemical shift - longer dwell time - but better signal to noise ratio). Narrow receive bandwidths accentuate this water fat shift by assigning a smaller number of frequencies across the MRI image. This effect is much more significant on higher field strengths. At 1.5 T, fat and water precess 220 Hz apart, which results in a higher shift than in Low Field MRI.
Lower bandwidth (measured in Hz) = higher water fat shift (measured in pixel shift).

See also Aliasing, Aliasing Artifact, Frequency Encoding, and Chemical Shift Artifact.

A 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. This signal will be mapped (wrapped, backfolded) back into the image at incorrect locations.
Foldover suppression (phase oversampling, no phase wrap) is a user-selectable parameter that maps this signal to its correct location outside the FOV, then discards any signal from outside the FOV before displaying the image. In order to be able to choose this parameter, in most cases more than an average is necessary.

See also Phase Wrapping Artifact and Oversampling.

(TRICKS) Time resolved imaging of contrast kinetics is a MRI technique, which increases the temporal resolution of dynamic contrast enhanced magnetic resonance angiography (CE-MRA) sequences. The K-space is divided into regions by increasing the sampling rate at the lower spatial frequencies and by reducing the sampling rate at the higher spatial frequencies. Since the time duration between two frames is shortened, it can be observed how frequently and how quickly the images are repeated at the exact same location.
TRICKS is particularly useful for dynamic vascular studies with high temporal resolution. TRICKS improves the calculation of the contrast bolus arrival and improves the characterization of arterio-venous malformations (AVMs).

See also Automatic Bolus Detection, MRA, Cardiac MRI.

Blurring comes most obviously from patient motion, but other mechanisms like low resolution sampling also lead to image blurring.