With regards to their molecular structures the Polymers may be either amorphous or crystalline.
When the temperature of a crystalline polymers lowers it undergoes the Crystallization (transformation of the liquid into a solid crystalline phase). In the liquid state the polymer molecules are disordered and can move freely whereas in the crystalline state they are arranged in the pattern according to a crystal lattice.
The crystallization process is reversible: a crystalline polymer may be crystallized and melted again unlimited number of times.
The temperature at which liquid-solid transition of a crystalline polymer occurs is called freezing point or melting point.
An amorphous polymer stays amorphous at any temperature however the mobility of its molecules changes sharply when the temperature reaches a certain temperature (glass transition temperature).
Below the glass transition temperature the molecules can not change freely their position nor configuration despite the fact that they are not arranged in a rigid crystal pattern. The polymer is amorphous in the glassy state but it is hard and relatively brittle.
Above the glass transition temperature the molecules become mobile. The polymers in such viscous state (rubbery state) are soft and flexible.
Most polymers are composed of both crystalline and amorphous portions (domains) which behave differently according to their structures: the amorphous domains turns viscous and soft when heated above the glass transition temperature whereas the crystalline parts melt when the temperature reaches the melting point.
The glass transition temperature (Tg) of a particular polymer in amorphous state is lower than the melting point (Tm) of the polymer in the crystalline state.