A 'Rotating Frame of Reference' is a concept to simplify the complex motions of a magnetization vector. The frame of reference rotates about the axis of the external magnetic field B0 (z-axis) at the Larmor frequency of the applied RF magnetic field B1. In this simplified concept the rotating vector B1 appears stationary.

A microscopic group of spins, which resonate at the same frequency. The spin precesses around a circle in the xy-plane and the net magnetization is the length, amplitude or magnitude of the magnetization vector Mxy: the quantity normally represented on a pixel-by-pixel basis in a MR image (thus amplitude or magnitude image).

A nonequilibrium state in which the macroscopic magnetization vector is oriented opposite to the magnetic field; usually produced by adiabatic fast passage or 180° RF pulses.

A pulse is a rapid change in the amplitude of a RF signal or in some characteristic a RF signal, e.g., phase or frequency, from a baseline value to a higher or lower value, followed by a rapid return to the baseline value. For radio frequencies near the Larmor frequency, it will result in rotation of the macroscopic magnetization vector. The amount of rotation will depend on the strength and duration of the RF pulse; commonly used examples are 90° (p/2) and 180° (p) pulses.
RF pulses are used in the spin preparation phase of a pulse sequence, which prepare the spin system for the ensuing measurements. In many sequences, RF pulses are also applied to the volumes outside the one to be measured. This is the case when spatial presaturation techniques are used to suppress artifacts. Many preparation pulses are required in MR spectroscopy to suppress signal from unwanted spins. The simplest preparation pulse making use of spectroscopic properties is a fat saturation pulse, which specifically irradiates the patient at the fat resonant frequency, so that the magnetization coming from fat protons is tilted into the xy-plane where it is subsequently destroyed by a strong dephasing gradient.
The frequency spectrum of RF pulses is critical as it determines the spatial extension and homogeneity over which the spin magnetization is influenced while a gradient field is applied.

A vector is a quantity characterized by a magnitude (in mathematics a number, in physics a number times a unit) and a direction (and a point of application), often represented graphically by an arrow. The length of the line segment represents the magnitude, and its orientation in space represents its direction. Vector quantities can be added to or subtracted from one another. Used in MRI to describe forces, e.g. magnetic moment, spin, magnetization etc.