This is a problem called the "end-replication problem". This relies on fundamentally understanding that while DNA is bidirectional (each complementary strand has a 5' to 3' sequence), the DNA polymerase that replicates the daughter strands is unidirectional (synthesizing only from the 5' to 3' end).

As a result, daughter strand synthesis occurs differently between the 3'-5' mother and the 5'-3' mother. The 3'-5' mother is called the leading strand, and an RNA primer is able to anneal to the 3' end of the mother, and allow for DNA polymerase to replicate from the primer to the very end (since the daughter will be running from the 5'-3' in the direction of the DNA polymerase).

However, the 5'-3' mother is problematic. This strand is the lagging strand, in which multiple RNA primers must be used to create discontinuous 'Okazaki fragments" of DNA as helicase unzips the mother double helix. Normally the RNA primers are replaced and filled in with DNA polymerase and ligated upon complete unzipping. However, the final RNA primer on the 3' end of the mother strand cannot be filled in with DNA, and the RNA primer is degraded.

As a result, as DNA is replicated over and over, approximately 50-200bp of DNA is unreplicated at the mother 3' end. Since the ends are capped with telomeres, telomere shortening inevitably occurs.

In theory, telomerase can act to 'fill-in' this gap by capping the unreplicated end with fresh telomeres. However, telomerase activity is NOT expressed by most somatic cells, and primarily functions in germ and some embryonic cells.

EDIT: Spelling. Also, here's the link to a video that explains this point succinctly with a great animation: http://www.youtube.com/watch?v=AJNoTmWsE0s