If you check a classic French cookbook for an old-fashioned recipe to make a bordelaise sauce or another so-called "brown sauce" for a steak, what you'll find is a recipe that calls for buying and cooking carrots, celery and a lot of other things (like beef bone marrow, which is not exactly sitting around in everyone's pantry). Demi-glace is a concentrated stock that has been produced from those kinds of ingredients so it enables you to leap-frog some of the time-consuming tasks that normally would be required.
Most importantly, using demi-glace will give a sauce the complex flavors that you would normally only get from a sauce prepared in a high-end restaurant.
I have tried several types of demi-glace, and I've compared two major brands that seem to be used widely by amateur cooks -- More Than Gourmet and Williams-Sonoma. I have cooked with both of them, and here's my view on how they compare in value:
Quality: Williams-Sonoma was the better demi-glace, hands down. Whether I used the chicken or veal demi-glace, it yielded a sauce that was superior to those produced by using More Than Gourmet's demi-glaces. The sauces created by using More Than Gourmet had less depth of flavor and more of an unpleasant, gelatinous texture.
Price: A 10.5-ounce jar of Williams-Sonoma's demi-glace costs $29 online or $2.76 per ounce. By comparison, a 16-ounce jar of More Than Gourmet's demi-glace (veal-beef) costs $39.50, which equates to $2.49 per ounce.
The Better Value: I think it is more than worth it to pay the extra 27 cents per ounce to use Williams-Sonoma's brand of demi-glace. You'll be much happier with the results. This Los Angeles Times blog also had good things to say about Williams-Sonoma's demi-glace.