It is a measure of leverage, and of how risky, or volatile, a company's operating income is.
Contribution Margin is a measure of operating leverage: the higher the contribution margin is (the lower variable costs are as a percentage of total costs), the faster the profits increase with sales.
Note that unlike other measures of operating leverage, in the linear Cost-Volume-Profit Analysis Model, contribution margin is a fixed quantity, and does not change with Sales.
The Degree of Operating Leverage (DOL) can be computed in a number of equivalent ways; one way it is defined as the ratio of the percentage change in Operating Income for a given percentage change in Sales (Brigham 1995, p. 426): This can also be computed as Total Contribution Margin over Operating Income: The above equivalence follows as the relative change in operating income with one more unit dX equals the contribution margin divided by operating income while the relative change in sales with one more unit dX equals price divided by revenue (or, in other words, 1 / X with X being the quantity).
Assuming the model, for a given level of sales, the DOL is higher the higher fixed costs are (an example): for a given level of sales and profit, a company with higher fixed costs has a lower Operating Income, and hence its Operating Income increases more rapidly with Sales than a company with lower fixed costs (and correspondingly lower contribution margin and higher Operating Income).
If a company has no fixed costs (and hence breaks even at zero), then its DOL equals 1: a 10% increase in Sales yields a 10% increase in Operating Income, and its operating margin equals its contribution margin: DOL is highest near the break-even point; in fact, at the break-even point, DOL is undefined, because it is infinite: an increase of 10% in sales, say, increases Operating Income for 0 to some positive number (say, $10), which is an infinite (or undefined) percentage change; in terms of margins, its Operating Margin is zero, so its DOL is undefined.