The sentence is from the start of the prologue. Here's some more context:
"Are they dead?" Royce asked softly. "What proof have we?"
"Will saw them," Gared said. "If he says they are dead, that's proof enough for me."
Will had known they would drag him into the quarrel sooner or later. He wished it had been later rather than sooner. "My mother told me that dead men sing no songs," he put in.
"My wet nurse said the same thing, Will," Royce replied. "Never believe anything you hear at a woman's tit. There are things to be learned even from the dead." His voice echoed, too loud in the twilit forest.
"We have a long ride before us," Gared pointed out. "Eight days, maybe nine. And night is falling."
I think it's sort of a double entendre. Literally, it means you shouldn't believe what you hear from the women who raised you. (They might be repeating old wives' tales.) But the sentence could also refer to sexual partners.
Ser Waymer Royce is young and arrogant. Like many of the characters in A Game of Thrones, he probably doesn't have much respect for women in general. His words are more dismissive than anything else. He wants to portray himself as courageous and manly, not like a (weak, scared) woman. As you will shortly find out, this does not end well for him.