Rockwool is a man-made fibre made from molten rock which is used as a growing medium and for seed germination in hydroponics. It can hold large quantities of water and air which aids the growth of roots and uptake of nutrients.
When used in hydroponic gardening, rock wool is called a substrate. A substrate is a material that supports the root system. Use can use several materials as a substrate, but not soil. It's probably the most widely used substrate in hydroponics.
The cubes are conveniently cut blocks that are very useful for seed germination.
Slabs are wrapped in plastic and are often used to transplant plants into, once seeds have germinated and started growing in cubes/plugs.
Plugs are round with a cut in the side or hole on the top into which a seed can be placed for germination.
Rock wool cubes and slabs and plugs come in different sizes. As a plant matures you can insert the smaller pieces into larger ones to support the larger root structure.
Grodan is the best known manufacturer and produces a full range of products.
When gardening indoors with rock wool, you should wear a face mask so that you don't breath in the harmful dust.