Telomeres are repeated DNA sequences which are found at the end of the chromosomes. To explain how important telomeres are an analogy between telomeres and the tip of a shoe laze, the aglet, can be made. If you remove the aglet, the whole shoe laze basically falls apart. The same with telomeres, as they get shorter after each cell replication, the integrity of the genetic material is in danger. And we do not care about losing telomeric DNA, since it does not code for proteins.
Telomeres main function is to protect the important genetic material, whose deletion would be fatal and could give rise to cancers and many malfunction. Most somatic cells, cells forming the body of an organism, have a life span of 45-50 divisions. This is due to the fact that after each cell division, telomeres get progressively shorter until the point that there is almost no more telomeric DNA to protect the genetic material, and the cell basically kills itself (apoptosis).
However, there are some cells that cannot be allowed to die, like germline cells, which give raise to gametes. If these cells died due to apoptosis, there would be no living thing on this planet. So how to overcome this shortening in germline cells?. The answer is telomerase. This enzyme is in charge of adding the telomere repeats at the chromosome ends so this cells do not die. However, there must be a balance in doing so… Most cancer cells are basically immortal because telomerase is always active. This is the yin and yang that is posed by telomeres and telomerase; they can make you immortal (like in the organism Tetrahymena) and they can give raise to cancers.