kingdom hearts birth by sleep and coded?

Birth by Sleep occurs 10 years before the first Kingdom Hearts game so I guess you could say it's a prologue of what happens. Little Sora and Riku make an appearance. The game also tells you a little bit more about the origins of the keyblade and the 3 knights who held them. One of them looks a lot like Roxas and he shows up in KH 358/2 Days too so I think he has a connection to Sora. I don't know much more about it but the game should explain it. Coded is a side game I believe. The events in the game do not have much of a connection to the other KH games as it technically doesn't actually happen. A digitized virtual Sora made by the King just goes on a bunch of missions. This takes place after KH2 when Jiminy Cricket sees a secret entry in the journey. To investigate they make this virtual Sora. That's pretty much it.

Well Deni (the other answerer is mostly right)

Birth By Sleep takes place 10 years before KH 1 a prequel. Its main characters the protagonist are 3 keyblade wielder, knights. Ventus who resembles roxas which Deni is right he has a connection to Sora. Terra who most likely has a connection with Xehanort and Aqua which her armor was seen in KH 2 FM in the Room of Sleep with Xemnas.

Then the two antagonist Master Xehanort who has connections with KH 1 Xehanort and the Dark Soldier who knowns about him.

Well anyway this game is going to explain Xehanort's past and the orgin of the keyblade.

Kingdom Hearts Coded plays a purpose similiar to Chain of Memories it leads up to KH 3. It takes place after KH 2. Which King Mickey digitized Jiminy the Cricket's journal after Jiminy finds out a mysterious message "We must save them from there torment" in the journal. By digitizing Jiminies journey a virtual sora is created traveling through worlds that were recorded in the journal. He must find the mysterious figure which is changing forms throughout the game. Such as this entity was in an Organization Cloak and another time was in KH 1 Ansem brown cloak