(MZ) Dimension in the direction of the static magnetic field (B0 and H0), in both the stationary and rotating frames of reference.

(T1) The spin lattice relaxation time (also called longitudinal relaxation time and T1 Time) is a spin property, whereby the value changes between different tissues. By the spin lattice relaxation process, the longitudinal magnetization Mz achieve the equilibrium value Mz0. The T1 time constant is an exponential approach toward Mz0.
The equation for the magnetization at a time t will be (if at t=0 the longitudinal magnetization is Mz0):
Mz(t) = M0+(Mz (0) - Mz0) exp(t/T1)

(IR) The inversion recovery pulse sequence produces signals, which represent the longitudinal magnetization existing after the application of a 180° radio frequency pulse that rotates the magnetization Mz into the negative plane. After an inversion time (TI - time between the starting 180° pulse and the following 90° pulse), a further 90° RF pulse tilts some or all of the z-magnetization into the xy-plane, where the signal is usually rephased with a 180° pulse as in the spin echo sequence. During the initial time period, various tissues relax with their intrinsic T1 relaxation time.
In the pulse sequence timing diagram, the basic inversion recovery sequence is illustrated. The 180° inversion pulse is attached prior to the 90° excitation pulse of a spin echo acquisition. See also the Pulse Sequence Timing Diagram. There you will find a description of the components.
The inversion recovery sequence has the advantage, that it can provide very strong contrast between tissues having different T1 relaxation times or to suppress tissues like fluid or fat. But the disadvantage is, that the additional inversion radio frequency RF pulse makes this sequence less time efficient than the other pulse sequences.

Contrast values:
PD weighted: TE: 10-20 ms, TR: 2000 ms, TI: 1800 ms
T1 weighted: TE: 10-20 ms, TR: 2000 ms, TI: 400-800 ms
T2 weighted: TE: 70 ms, TR: 2000 ms, TI: 400-800 ms

See also Inversion Recovery, Short T1 Inversion Recovery, Fluid Attenuation Inversion Recovery, and Acronyms for 'Inversion Recovery Sequence' from different manufacturers.

(Mz) The component of the net magnetization vector in the direction of the static magnetic field (z). After RF excitation, this vector returns to its equilibrium value at a rate characterized by the time constant T1.

Signal intensity interpretation in MR imaging has a major problem.
Often there is no intuitive approach to signal behavior as signal intensity is a very complicated function of the contrast-determining tissue parameter, proton density, T1 and T2, and the machine parameters TR and TE. For this reason, the terms T1 weighted image, T2 weighted image and proton density weighted image were introduced into clinical MR imaging.
Air and bone produce low-intensity, weaker signals with darker images. Fat and marrow produce high-intensity signals with brighter images.
The signal intensity measured is related to the square of the xy-magnetization, which in a SE pulse sequence is given by
Mxy = Mxy0(1-exp(-TR/T1)) exp(-TE/T2) (1)
where Mxy0 = Mz0 is proportional to the proton or spin density, and corresponds to the z-magnetization present at zero time of the experiment when it is tilted into the xy-plane.

See also T2 Weighted Image and Ernst Angle.