This tool is a special one in Sketch. It’s not in the toolbar by default, but you can add it by Control-clicking the toolbar and choosing “Customize Toolbar…”. It’s also available in the menu under Layer › Path › Rotate Copies.
This tool takes one layer and rotates copies of it around a certain point. Take the example of a flower; create just one leaf shape, then rotate a dozen copies around the center and you’ll have your flower.
Select a layer, activate the Rotate Copies tool, enter the number of copies and close the dialog. Then position the point where you want it and press the Escape key to confirm.
If you’re using Sketch 53.1 or earlier, the Rotate Copies tool creates a compound shape, where all shapes will be added as subpaths to the original shape. If you’d rather have them as completely separate layers, choose Layer › Combine › Break Apart in the menu to turn them into separate layers.
In Sketch 52 or newer, the Rotate Copies tool doesn’t create a compound shape and instead creates (and rotates) separate copies of the shape. You can select all the shapes and use the “Union” Boolean operation to get the same result as earlier versions of Sketch.