The surround is the ring of soft material at the outer perimeter of the woofer. It allows the stiff cone to move in and out to produce sound. It needs to be both flexible and air-tight, without any holes or tears. Over time, materials used for the surround can become brittle and crack, or otherwise degraded or damaged. The problem is worst with foam-type materials, less so with synthetic rubber types.
I had Snell Es that needed the surrounds replaced, but I don't recall the type of surrounds they needed. Snell were very proud of the close-tolerance matching of all their parts - try to find a genuine proper replacement, rather than a generic. The process to replace the surround material is fairly straightforward, requiring only a suitable replacement part, proper adhesive, and steady hands. Often you can find folks to do it for a reasonable price as a small business. There's a fellow local to me who advertises on Craigslist, for example.