Hunting hounds are bred and used for different skills. There are hunting dogs used for their ability to scent things, some for their ability to see better, and some for their ability to dig into burrows. We don't know what the Talbot was used for, but the short legs and large feet would make it good for digging.
The Talbot was linked to John Talbot, 1st Earl of Shrewsbury (the kneeling man in this post with a Talbot Dog behind him). Henry VI called him "Talbot, oure good dogge." This may have to do with Talbot's "doggedness" at pursuing the French during the Hundred Years' War. Or just a joke. The Talbot is not on the coat of arms of either the Talbot family or the Earls of Shrewsbury until much later than the 15th century. (Regarding heraldry: the Talbot and the greyhound are the only two dogs found in English heraldry.)
Talbots seem to have died out by the end of the 18th century. The only place they are seen now besides heraldic emblems is on signs for public houses. You can also see a Talbot carved in stone at Canterbury Cathedral in the coat of arms of one-time Archbishop of Canterbury and Lord Chancellor of England Simon Sudbury. You can see Simon himself—or rather, his skull—at a different church. That's a story for tomorrow, however.