A telomere is a region of repetitive DNA found at the ends of all eukaryotic chromosomes (and some prokaryotic chromosomes; notably those that aren't circular). In humans, the consensus sequence of telomeres is as follows:

5' TTAGGG 3'
3' AATCCC 5'

This sequence may be repeated up to 2000 times in a single telomere.

Telomeres exist to protect the ends of chromosomes from being shortened during DNA replication. Because DNA replication must occur in a 5'-->3' direction, if the chromosomes were not capped by additional stretches of DNA in the form of telomeres, then the ends of the chromosomes would not be replicated (as there wouldn't be sufficient template material). Telomeres 'self-sacrifice' so that they are shortened in successive rounds of replication, rather than the important genetic information in chromosomes. Because most prokaryotic chromosomes are circular, they do not suffer from the loss of genetic information in the same way and thus do not have telomere regions (although the minority of prokaryotic chromosomes that are linear, do).

When cells are left in culture, they replicate and divide for a few rounds of mitosis before their telomeres are completely shortened and the cells die. This phenomenon is called
replicative senescence. In somatic cells the lifespan of telomeres is far longer due to enzyme telomerase. Telomerase adds repeats of TTAGGG on to the 3' end of existing repeats in order to maintain telomere length. Telomerase is often cited as the key to cell immortality, and is often found in higher than usual concentrations in cancerous cells (cancerous cells are, left alone, immortal).

Telomerase is a ribonucleoprotein particle, meaning it contains both protein and RNA subunits. While the protein subunit acts as a reverse transcriptase, catalysing the conversion of RNA to DNA, the RNA component serves as a template for the DNA telomere to be based on.