Explain why DNA is a store of genetic information, and how the base pairings are important?

I will answer your two questions in reverse, because it
makes more sense that way.

The base pairings are important,
because each 3 base sequence gets transcribed into a 3 base Codon on an mRNA molecule. 
This mRNA molecule leaves the nucleus of the cell and travels to a ribosome.  The
ribosome reads each Codon and pairs it up with the Anticodon of a specific tRNA
molecule.  For eacmple:

DNA:  ACG --> mRNA:  UGC
---> tRNA: ACG 

Each specific tRNA molecule (in this
case, ACG) carries a specific amino acid (in this case, threonine).  As the mRNA
molecule is thus translated by the ribosome, a long chain of amino acids, arranged in a
specific order, is synthesized.  This chain of amino acids, called a polypeptide, will
then be transported to the Golgi Body where it is processed and will become part of a
protein.  And proteins are used by your body to build structures (hair, muscle,
hemoglobin, etc) and enzymes (which regulate all the metabolic
processes).

So, the short answer:  DNA stores the
information used to build proteins.  The specific base pairings code for specific amino
acids that build these specific proteins.  If you have the wrong base pairing, you will
most likely get the wrong amino acid, and thus the wrong protein.  This is called a...
mutation!