If you embroider a story or account of something, or if you embroider on it, you try to make it more interesting by adding details which may be untrue. He told some lies and sometimes just embroidered the truth She embroidered on this theme for about ten minutes. = embellish
If something such as clothing or cloth is embroidered with a design, the design is stitched into it. The collar was embroidered with very small red strawberries Matilda was embroidering an altar cloth covered with flowers and birds I have a pillow with my name embroidered on it