Shipping classes are used to group products of similar type (weight, warehouse, box size, etc) and used by some shipping methods, such as table rate shipping or flat rate shipping, to provide different rates to different classes of products.
For example, with shipping classes and WooCommerce standard flat rate shipping, it’s possible to create different flat rate costs for heavy items and small parcels. If you use Table rate shipping plugin, you can offer more complex shipping options using the shipping classes along with shipping zones and other order parameters.
Hore’s a guide on how to set up shipping classes in WooCommerce.