Nuts in general can represent toughness due to their hard outer shell. Seeds in general can represent fecundity and fruitfulness as per their nature- but walnuts in particular are a potent symbol of masculinity. While often the nut is thought of as endurence to hardship (seeing a nut broken can be a collapse of defenses) breaking open a nut can also be a good omen - it can represent breaking through the hardships - if the nut is healthy or tasty inside, than take it as a hint that your labors will pay off, and that the struggle was worth it - If the inside is rotten or bitter, than this may symbolize fear and possibility of plans falling through, or hard work not paying off.
Walnut's three most potent meanings are of sexuality and toughness - and even though all nuts can be reminiscent of manhood, walnuts in particular are 'the manliest nuts'. Well, in vegitation, anyway.