Eyedropper Tool is the tool with which you can easily do many things: from simply copying solid colour to copying gradients, shapes and other properties from one object into another one.
These tools allow you to copy properties from one object to another. Click on an object A with the eyedropper tool to sample its properties and next take the paint bucket tool and click on another object B to transfer the A' sampled properties to B.
Although eyedroppers tools in graphics software are mostly used to sample colors, the eyedropper tool in CorelDraw can sample a lot more properties beside color such as line style, skew, rotation, effects applied to the object and fonts for text objects. You can select the properties which are sampled and transferred with the active property bar.
A quicker way to transfer some basic properties from one object to another is to right click on object A and while holding the right mouse button, drag and drop object A on object B. When you release the right mouse button a menu will appear with a few options select "copy fill here", "copy outline here" or "copy all properties" to transfer fill, outline or all properties respectively from object A to object B.