Basic Information
This is a grenade designed to be fired from the muzzle of a long arm - usually a rifle1. These weapons are generally a historical artifact these days and have been becoming less and less popular since the grenade launcher was reinvented, although some nations still issue them or hold an inventory.
Some designs consist simply of a hand grenade with a little extra propulsion (and hopefully a longer time fuse), driven either from a cup like adaptor fitted to the muzzle of the rifle or a rod inserted into the barrel and attached to the bottom of the grenade. These have the small problem of needing (at least one) adaptor and relatively poor ballistic performance and require the user to be issued with a seperate supply of bulletless propellant cartridges which he must be absolutely sure to use instead of live rounds when firing the grenades.
More advanced designs are 'rocket shaped' creations that clip onto the rifle's muzzle adaptor - at first these also required blank propellant cartridges but the most recent (the final?) generation worked on a 'bullet trap' principle with live rounds.
These weapons were born from WW1 and the desire to reliably "throw" grenades across no-mans land into an enemy trench. In practice they weren't much used for this and ended up competing for the niche with mortars. And losing. Still, they persisted into WW2 where they also picked up a limited role as a (fairly ineffective) anti tank weapon.
After the end of WW2 the rifle grenade slowly began to drift out of favour, driven into obselescence by grenade launchers and light mortars and by the early 21st century is more or less a gimmick.
In their time rifle grenades have been manufactured in pretty much every flavour that grenades come in, plus flares, message carriers and line bearing munitions - although few nations will issue more than one or two kinds.