Genetic diversity is the fact that the organisms have differents genes or versions of it (allele).
You can be homozygot and get twice the same allele (example : O blood type) or being heterozygot and get two different alleles (ex : AB blood type).
Crossing-over happens during the meiosis when the pair chromosomes cross-over each other and some genetic exchanges may happen so it can create new allelic combination in the gamete and then if it leads to a new individual after fecondation development etc…. get an individual to have new allelic combination and maybe give him advantages disadvantages or none of them !
But there will be a new allelic combination and so genetic diversity got increased.
Hope it helps you ! 🙂