How does the stealth address thing work?
A stealth address is a way to
collect money anonymously, where only you and the sender know both participants in the transaction.
When you make a new receiving address, you can select the option to create a stealth address. A stealth address is a very long address that allows the sender to make a one-time address that belongs to the stealth address. It is practically impossible for a third party ("adversary") to link the stealth address to the one-time address based just on the addresses alone. Because senders can create practically unlimited stealth addresses, you can receive unlimited payments that can not be linked to the stealth address.
It is also practically impossible for an adversary to link any two one-time addresses without some additional information that comes from how you send coins. It is important that you be careful how you spend funds that get payed to your stealth address because addresses can be linked if you combine them when making a payment yourself. Coin control is good for preventing, or at least reducing, this kind of linking.
Unless you are very, very careful about coin control, I do not recommend relying on stealth addresses for anonymity. However, stealth addresses are very useful because they provide a way to perform a cryptographic key exchange called a Diffie-Hellman key exchange where only the sender and recipient know the exchanged secret key. This means it is possible to create an encrypted message with a very strong cipher that uses the same encryption and decryption keys ("symmetric cipher"). This strong symmetric cipher enables a sender to encode encrypted messages in the block chain. This is exactly the technology we use for the pump group pick, where we provide the pick information in tiers. Even though the pick is sent to a participant in the block chain, only the participant (and sender, who knows the pick anyway) can decode the pick.
Disclaimer: Although it has anonymity features like built-in tor and stealth addresses, Synergy is not a coin focused on anonymity. Synergy's anonymity features are considered "light weight", to protect users from small-time hackers. For example, it would take a government to find you through your Tor address, but no hacker without government-scale resources could do it.