Laurus nobilis is the "Bay laurel" used in cookery.
Umbelularia Californica, the "California Bay" is at least edible, though unpleasantly more pungent than Bay laurel. Some gardeners call it the "headache plant" (sniff some crushed leaves and check it out).
Prunus laurocerasus, the "Cherry laurel", is used in hedging and is probably the one you are pruning.
Do not eat Cherry laurel. It is toxic enough that the crushed leaves are used in field entomology to kill insect specimens. A tummy ache is probably the worst you'd get if you seasoned with it, but the flavor would not add anything good.
Regular hedge laurel (prunus) is not edible (my Sunset garden book says it's actively poisonous). Bay laurel (laurus) is a completely different plant with extremely fragrant leaves, hard to mistake for anything else. California bay laurel (umbellularia) is often sold as cooking bay although its flavor is different from true bay laurel. If you're not sure, don't eat it!