Okay, I thought I'd take a shot at this and maybe give a more detailed answer. I am answering this from a Doubles perspective.
What do Safety Goggles do?
Safety Goggles stop the damaging effects of Sand and Hail. They also block Spore and Powder moves.
But how does this help my Zapdos?
Well, the Safety Goggles let Zapdos function on a Sand or Hail team (but most commonly Sand). This lets Zapdos partner with common Sand-abusing Pokémon like Tyranitar, Excadrill and Mega Garchomp. All of these guys love to spam Earthquake, and having a partner who's immune to both their spread attack and chip damage is a huge plus.
Not only that, but Safety Goggles also offer an immunity to all Spore and Powder moves, the most common being Spore, Sleep Powder, and Rage Powder. Wait a minute, what two common VGC threats does this cripple majorly? Amoongus and Mega Venusaur (and to a lesser extent Volcarona and Breloom, but the former do their jobs better).
Amoongus' job is to redirect attacks aimed at his partner with Rage Powder while they set up and, often, Spore the opposition. However, Zapdos come fully equipped to destroy Amoongus. Safety Goggles render both Spore and Rage Powder ineffective, allowing a partner to clean up the opponent while Zapdos deals with Amoongus through Heat Wave or Hidden Power Ice.
Mega Venusaur is an infamous bulky Sleep inducer. While Zapdos has a hard time KOing Venu by himself, he can easily switch into a predicted Sleep Powder while his other teammate closes shop.
Woah, Safety Goggles are amazing!!
Yes, yes they are.
WARNING! Do not just slap Safety Goggles onto everything in sight. Always consider if there is a better item option. For example, you would never see Safety Goggles Landorus because he is much, much better with Choice Scarf or Assault Vest. The Goggles might not even be the best item for Zapdos, either. If your team is not a Sand/Hail team, or you have no problem stopping Rage Powder and Spore, then consider a Sitrus Berry or Rocky Helmet instead.
