Specifically, this is a specialist sleeve-badge of the Stahlhelm denoting the wearer's former arm of service in WWI; in this case, Infantry. Some people attempt to call this a Sturmtruppen specialist badge because of the grenade. But, since I've never seen one with just crossed rifles (for infantry), I have always dismissed the Sturmtruppen identification as an attempt to "value add" the badge.
There are perhaps 9 or 10 different badges in different designs for various specialties.
Althought this one is by far the most common, they are all quite scarce and it's nice to find it complete with the backplate and proper blue cloth backing.