Coping saws are C-shaped handsaws used for delicate woodworking such as creating cutout shapes in wood or making coped joints in moldings. The blade is a thin piece of metal that stretches across the open end of the C. When the blade becomes dull, it's no longer useful for accurate and easy cutting. Plus, it's more dangerous since you exert more force trying to get it to cut; more force means a greater chance for you to slip and cut yourself.
While you might be inclined to sharpen a dull coping saw blade as you would on some of your other saws, it's not usually worth the effort. You can sharpen some blades, like those with steel teeth, on your own. But blades with carbide-tipped teeth have to be sharpened by a professional. A professional will usually tell you when your blade isn't high enough quality to warrant sharpening. Considering that a multi-pack of new coping saw blades costs just a few dollars, it's probably not worth the effort to fix an old blade. However, you can hang on to used, dull blades for when you're working on some kind of demolition project and you don't want to ruin your good saws.
To prolong the life of your coping saw blade, you should wrap it up when it's not in use. An easy way to protect your blade is to slice open a section of hose or tube and insert the blade into the slit. Also, before embarking on your coping saw project, double check that the material you're going to cut is free of nails that might damage the blade. Make sure it's clean so that no abrasive substances will wear away at and dull your coping saw blade.