How chromosome number remains the same in the members of the same species?

We'll use humans as an example since it's simple and relevant.

All healthy humans have 46 chromosomes (23 pairs of very similar chromosomes). When gametes are formed in meiosis, this number is halved, such that sperm and ovum have only 23 chromosomes (just one of each pair). When these gametes meet and fuse as a result of sexual reproduction, the 23 chromosomes from the ovum and the 23 chromosomes from the sperm combine to form the full set of 46.

Sometimes meiosis doesn't quite work perfectly, though. Downs Syndrome is an example of this (one gamete has both copies of chromosome 21, so after fusion with the other gamete there are 3 chromosome 21s!).