DNA is a nucleic acid. It is responsible for storage, expression, and transmission of genetic information. Basically you have 2 strands, each one is composed of sugar phosphates (making up the "sides of the ladder") with nitrogenous bases connecting these two strands. The bases (also known as nucleotides) include adenine, guanine, cytosine, and thymine. Adenine matches with thymine, guanine matches with cytosine (most of the time. They can mismatch; this is called a mutation.)
The expression of genetic information is due to the long chain of matching nitrogenous bases. Each gene is responsible for the synthesis of a polypeptide. Originally it was believed that one gene was responsible for an enzyme, but that belief has since been modified. So you have all these genes which are responsible for polypeptide synthesis, and these polypeptides are responsible for all kinds of things that go on in the organism in question. If there is a mutation somewhere in the DNA, the gene may not be coded correctly for the polypeptide it is supposed to be responsible for.
There are a lot of reasons why mutations can take place. One example is the effect old age has on telomeres. The telomere is the region of repetitive DNA at the end of a strand. It prevents mismatches in the nucleotide sequence when DNA is replicated. Over time, the enzyme that replenishes telomere (telomerase) loses functionality. This can cause mismatches to occur during replication. The telomeres will become extremely short. A lot of cancerous cells have short telomeres. Note: telomerase function is not completely lost. That would likely cause the cell to die, which happens if the telomeres get too short.
To summarize:
DNA is responsible for storage, expression, and transmission of genetic information
Long chain of nucleotides make up the "genetic code"
Mutations can happen in a number of ways, and can have innumerable effects on the organism in question
Cancerous cells are an example of a cell that has undergone some sort of mutation
