Upcycling is to reuse materials that would have been thrown away. This could be by-products from an industry, such as scraps of cloth from a clothing factory, saw dust from a wood cutting mill, containers used for shipping that are not needed after the shipment was received, products that are worn out and in bad shape, or any unwanted products by anyone. Then someone gets these waste products and transforms them into new products.
Upcycling is not the same as recycling or downcycling. To downcycle is to recycle and convert materials into lesser value materials. For example, plastic bottles can be melted down and made into new plastic that might be of lesser quality than virgin plastic so you might use them mixed with other materials in things like carpet. In downcycling, you smash and grind or melt and try to use the base material but also spend energy doing it, and it typically is of lesser quality than the original product.
Upcycling, on the other hand, is like taking the plastic bottles and creating a piece of artwork out of them without altering them much. Using reclaimed wood is upcycling: you take old wood from another building and use it in a new building with minor improvements. To downcycle or recycle that wood would be to grind it down into a sawdust and create particle board, which is not as strong and takes a great deal of energy to make.
Another example is secondhand clothing, which typically just needs to get washed and lightly repaired to be in good enough condition to be sold again. Compare this to the energy required to break down that fabric and recycle it to spin new fabric completely.