Kadena uses 20 different chains to compose its "chainweb". Addresses have an individual balance on each of those chains, and it's possible to send KDA from one chain to another. Under the hood, this requires one transaction destroying the asset on the source chain, and a continuation transaction creating the asset on the destination chain.
When sending from your Koala Wallet, below the destination address you must choose the destination chain as requested by the receiver. On the next step you choose which chain to send from. If the source and destination chains are different, sending will initiate a cross-chain transaction. Koala Wallet will automatically take care of the transaction pair. You don't need to do anything, just send like any other transaction.
Due to necessary extra step, this process can take a few minutes to complete. After sending a cross-chain transaction, please be patient and wait for the second confirmation.
When that's done, you will see two transactions in the wallet's history, one for each chain, each with its own ID. A future update will combine them into a single entry to better reflect the single operation and balance change.
To re-manage your funds between chains, you can simply send to yourself choosing the appropriate source and destination chains.
Please note that some tokens currently cannot be sent cross-chain. In those specific cases Koala Wallet will alert you and prevent you from sending.