Annealing refers to the use of a heat treatment to alter a material. A polymer is heated to a temperature above some transition temperature for an arbitrary amount of time to change its morphology, and then cooled.
For glass, annealing removes internal stress.
For metal, annealing alters the microstructure, changing properties such as strength and hardness.
For an analogy, imagine that in the cold of winter (temperature < 0°C) you have a bucket filled with snow. You bring it into the house, it heats up, and the snow melts. You take it back outside, and it cools down to the outside temperature, 0°C. The optical properties have changed. The density has changed. The mechanical properties have changed. Annealed snow becomes solid ice.
Annealing the sample may give a DSC spectrum better peaks. On this note, the thermal history of the sample needs to be known, because annealing can alter the spectrum. It may be a standard practice to take two DSC spectra. The first spectrum is taken to anneal the sample, and the second is taken to have a "post-anneal" spectrum.
If a semi-crystalline polymer has not yet achieved its thermodynamic limit of crystallinity, then annealing above the glass transition temperature increases the crystallinity (the crystalline regions grow).
Exact temperature and time requirements to achieve complete crystallinity may be determined by a DSC experiment.
Annealing relieves the internal stress in a polymer. A friend who was just starting work with polymer composites reported that a polycarbonate "exploded" when it was heated. The "sudden transition", which startled the operator, was attributed to relieving internal stress.
Cold drawn polypropylene fibers annealed at 140ºC reestablished a monoclinic structure. This structure had been lost during the cold drawing process.
Annealing affected the performance of polymer light emmitting diodes. Annealing above the glass transition temperature improves the efficiency of hole injection and unfortunately reduces photoluminescence efficiency.