Polymerization of acrylamide proceeds on the basis of free radical catalysis. Therefore, TEMED catalyses the decomposition of persulfate ion to give a free radical which will react with monomeric acrylamide ( sometimes with bis-acrylamide depending on the ratio of two monomers) forming a single bond between two monomeric units.
It is very nicely explained in Principles and Techniques of BIOCHEMISTRY and MOLECULAR BIOLOGY. Edited by Keith Wilson and John Walker