If you wish to better organize your products (add / edit / remove) and also arrange them under Categories, for a better product management, please use the Inventory section, at the top:
Here, you will find 3 main sub-sections, pretty self explanatory:
1. Products – where all your products are listed (for more info on how to add a product, please click here)
2. Add Category – allows you to add new categories of products to your inventory
3. Categories – lists all the categories
If you wish to change the category where a product is listed, you will simply need to click on the product, scroll down to Categories and choose a different one from the drop-down.