Just digging around BitCoin Explorer and I came across a neat transaction. More so, curious, does the second output where it lists "Not yet redeemed" mean that someones BitCoin wallet didn't accept that transaction or something?
No, it means that those coins are not yet spent.
Bitcoin transactions work with inputs and outputs. Every transaction can have one or more inputs, and it may then create one or more outputs of which the total amount adds up to the sum of the inputs (minus the transaction fee).
Only coinbase transactions do not require inputs. Those are the first transaction in every block that gives the miner of the block his block reward and all the fees from the transactions in the block.
When you want to spend bitcoins from one of your addresses, you will have to find an "unspent transaction output" for that address, make a transaction with the output and assign new inputs.
What this means is that an address does not really have a balance stored in the block chain. There is just a list of unspent outputs, and those that are bound to some address add up to this address's balance.