In baking, as above, "glaze" generally refers to a smooth, glossy finish.
Painting bread dough with a bit of beaten egg (also called an egg wash) will result in a browner, shiny crust (as in challah).
Most often, a glaze is essentially a thinned-down frosting. This comes in handy when you're in a hurry or find yourself with a cookie or cake which is a little underwhelming in flavor, or simply undersweetened. I'm a fan of tart desserts, but occasionally I've overdone it with the lime juice in cookies and ended up with something too intense, but rescuable with a sugar glaze to balance the flavor.
Some recipes fancy it up with a bit of butter or flavoring extract, but almost all glazes simply consist of powdered sugar whisked with enough water, milk, or fruit juice to create a workable consistency. Leave it a little thick if you want to smear it on cookies, thinner if you want it to drip down the sides of a Bundt cake.
I have never tried it, but I feel like an almond cake with an orange or grapefruit glaze would be stupendous.