Conversational shorthand meaning either "My source for this information would take too long to explain" or "I'm not sure where this information comes from".
"They say that the sky is blue from Rayleigh Scattering."
"They say that the reason capsaicin burns is because the capsaicinoid crystals get lodged in the taste-buds and shred them at the microscopic level."
"They say your mother is a dirty ho."
When you hear "they say" take what they say with a grain of salt.