Spies are people that will be in a guild and give information to the enemy (usually in war time ) of attack plans, weaknesses, etc. Sometimes spies are long-time members of the guild they are spying on but have gained a motive for helping the enemy, but more commonly they are just a player sent in the enemy guild when information is needed. They usualy get information about Strongholds, Jumpgates whats in a fleet, and so on.
It is virtually impossible to discover spies in a guild, oftentimes leading to paranoia. One simple solution that was suggested is to have a players former guild shown on his profile.