When creating a map, there are many times that you have more than one layer. When adding them to the Map, they are added in the order in which they were last edited. This is due to AmigoCloud's decision to make the most commonly edited layers easier to access for the users.
However, when creating a map, there are many more considerations to keep in mind. For example, reference layers are usually below data layers. Also polygon layers are below lines, which are below points. For example, Building names will be on top of road lines, which will be on top of city boundaries.
So to reorder the layers, in the layer view, you can select them and drag them to a new location. Here I am ensuring my "Countries" layer is below my "Bucket List" Layer.