The return of excited nuclei from the high energy state to the low energy or ground state is associated with loss of energy to the surrounding nuclei. Nuclear magnetic resonance was originally use to examine solids in the form of lattices, hence the name "spin-lattice" relaxation. Macroscopically, T1 relaxation is characterized by the longitudinal return of the net magnetization to its ground state of maximum length in the direction of the main magnetic field. The rate of return is an exponential process as is shown in the following figure.
The T1 relaxation time is the time for the magnetization to return to 63% of its original length. After two T1 times, the magnetization is at 86% of its original length. Three T1 times gives 95%. Spins are considered completely relaxed after 3-5 T1 times. Another term that you may hear is the T1 relaxation rate. This is merely the reciprocal of the T1 time( 1/T1). T1 relaxation is fastest when the motion of the nucleus (rotations and translations or "tumbling rate") matches that of the Larmor frequency. As a result, T1 relaxation is dependent on the main magnetic field strength that specifies the Larmor frequency. Higher magnetic fields are associated with longer T1 times.