Profit margin is simply profit divided by sales. This means that there are as many measures of profit margin as there are measures of profit. It is usual to be specific and refer to gross margin, EBIT margin, operating margin, EBITDA margin, etc.
Profit margins can provide a comparison between companies in the same industry, and can help identify trends in the numbers for a company from year to year. In the latter case it separates the effect on profits of growth or decline in sales from changes related to efficiency and price levels. It does not do this perfectly as margins naturally increase with sales (this is called operational gearing), particularly when a company has a high level of fixed costs or high sales growth or decline.
The difference between the gross and operating margins is the overhead cost ratio.