Natural latex is a polymer - that is, it is a long molecule composed of many repeating smaller molecular units. Charles Goodyear first discovered a process that made rubber commercially useful. The story is that he accidentally dropped a mixture of rubber and sulfur into a fire. This produced a material that was no longer sticky, and had many desirable physical characteristics. Goodyear named this process vulcanization, after Vulcan, the Roman god of fire and craftwork.
Vulcanized rubber is stronger yet also more elastic than the starting material.
The sulfur cross-links the polymer chains in the latex. You can stretch vulcanized latex, but the polymer chains then snap back so the product returns to its original shape. Nowadays, latex gloves are not produced with sulfur and fire. But sulfur is still very important as the primary vulcanizing agent. Accelerators are chemicals that speed the cross-linking process, either by donating sulfur atoms or because they are soluble within the natural rubber and help to draw the sulfur into the rubber by binding with sulfur.