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".
Examples include:
"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.