Blocking a player directs the games matchmaker to not put you and the blocked player in the same instance. Once you have blocked someone you need to quit the game and restart it, for it to take effect. If they are friends with someone in the same instance with you, the games matchmaker will put the blocked player in your same instance. It's doing this because it ignores who you have blocked in order to keep players that are friends in the same instance. A blocked player cannot see a list of who has blocked them. They can still see your chat messages and they can respond to you in the Comms Channels.
You are only able to Block a player when they are in the same instance as you, when they post a message in a Comms Channel or accepts your friend request. Which means you have to have contact with this player in order to block them. There are two ways you can Block a Player, through the in game Comms Panel and in the Main Menu under Friends and Private Groups.
Blocking a Player in the Comms PanelEdit
If you see their name in the Comms Panel you can select it, then select to block them. This works no matter what type of chat they use, Local or System. The System Channel allows communication between game modes like Solo, PG's and Open. So you can block and Open player while you are in Solo or a PG, if they chat in the System channel without risk. Also if their name appears in the Local player list you can also select their name then select Block to block them. However, they have to be in the same game mode as you are, Open or the same PG.
Blocking a Player in the Main Menu under Friends and Private Groups.Edit
To block a player in the Friends and Private Groups panel, you first must send them a friend request. Once they accept your friend request you can go to their name and select block, then you can unfriend them. Issues with this means they have your player name and can retaliate through other means. They might be keeping a list of names of players that do this, and often they have friends and other accounts they can use to hunt a player down.