Was that intended to be used/hunted or was it a display of design and manufacturing capability? Built just because...why not, it's cool and we can.
Probably intended for driven bird shooting, as KyJon speculates. A hunter could fire four shots before needing to reload. It could be the origin of the term" Game Hog". Naturally, it would cost more due to the greater difficulty in building, and the more complicated firing mechanism. At 7 lbs. 7 oz., I'd guess the barrel and chamber wall thicknesses of the 4 barrels might cause some here to swoon. But surely it passed proof.
This is the first four barreled English shotgun I've seen, but four barreled guns were more common in Germany, Austria, and other parts of Europe. The 4 barrel guns from Germany were called Vierlings. 3 barrel guns are Drillings, and they are fairly common. 5 barrel guns are called funflings. They were built in all manner of barrel configurations. Some were all shotgun barrels, but most are some combination of shotgun and rifle barrels. A well heeled hunter could have a single gun that had shotgun barrels for birds, and also had a rimfire barrel for small game, and one or more centerfire barrels for deer, stags, wild boars, and other larger game. He could essentially shoot any game that might run or fly by, all with one gun.