Hi,
When you add characteristics to a product, hikashop will generate variants for each combinations of the values of the characteristics. If you already had variants before adding a new characteristic to a product, hikashop won't generate all the variants as it would have to delete the existing variants for that. So it doesn't do it but you can still do it manually via the manage variants button. Otherwise, you can jsut remove all the variants of your product. Then, remove the characteristics from your product and save it and then add your characteristics back. That will recreate all the variants automatically.
In the characteristic table, you have one entry per characteristic as well as one entry per value of characteristic. Then, in the product table, you will have the main product and one entry per variant. In the variant table, you will have one entry per characteristic value per variant plus one entry per characteristic for the main product. That's what links products/variants and characteristics