Recycling is a better known concept than upcycling, however are different concepts.
Recycling is recovering a product that has been used and putting it through a process to enable the material of the former product to be used in production of new products. An example of this can be the paper recycled at schools. This paper gets recycled into either paper for use in printing again or paperboard for use in packaging. Recycling can happen many times over depending on the quality of the material. Paper consists of paper fibers and usually these fibers can be cycled back to printing material 8 times. After that, the fibers get too short and then it becomes suitable for paperboard.
Upcycling is using various different products to make something new, but for different purposes. For instance, you can make bags from your old jeans. This is giving a new life to the jeans and extending the length of time you can use it. However recycling would be turning the jeans back into jeans. Upcycled items might still be recyclable at the end of their second life depending on the item in question.
