How does offspring have a genetic variation

Through the process of meiosis. During meiosis, crossing-over occurs and increases genetic diversity. The haploid cells formed from meiosis (sperm or egg) have half the chromosomes so when the two meet they combine and share different chromosomes.

They have a variation because when two parents combine their genes, the offspring gets some from both and it continues every generation; getting traits and genes from all over the gene pool. Every person is different and has a unique set of genes, so when they are passed off, the offspring literally just has a bunch of everything