Cell Cycle and Cell Division

Telomeres are the specialised ends of the linear chromosomes of eukaryotes.
They consist of a highly conserved, short repetitive DNA sequence; in humans it is (TTAGGG)n, repeated many times.
They seal the ends of the chromosomes, so that the ends are not recognised as broken DNA and do not fuse with other chromosomes or get degraded by nucleases.
They also compensate for the shortening of DNA at every round of replication; the enzyme telomerase adds the repeats back.
In this way telomeres maintain the stability and integrity of the chromosomes and prevent chromosome loss.
They do not initiate transcription, they are not responsible for the pairing of homologous chromosomes, and they do not act as origins of replication (replicons).
So they control chromosome function because they prevent chromosome loss.