Blockexplorer only shows confirmed transactions, as it scans the blockchain to get it's information.
BlockChain.info will show you unconfirmed transactions. I'll explain.
Bitcoin transactions are transmitted on a peer-to-peer network. When you transfer bitcoins, that transaction is sent from one host to the next to the next. At this point, the "unconfirmed" transaction exists on the network.
When the Bitcoin miners start to build a block, they gather up all of these unconfirmed transactions from the network, verify them, and combine them together in a block. Then it "mines" the block. (Mining is the time consuming part.) Every 10 minutes or so, a miner gets lucky and finds the lucky number to mine their block of transactions. It transmits this completed block back out to the peer-to-peer network. At that point, the transaction has 1 confirmation. That block signature is included in the next block of transactions 10-20 minutes later, and that adds another confirmation.
If the Blockchain information site you use shows unconfirmed transactions, then they are showing you transactions that have been transmitted across the p2p network, but not included in a block yet.
So here's the rub. A block can only be so big and miners want to make money. When a miner is picking what transactions to include in a block, they prefer the ones that pay the most. There are a lot of * transactions that need to be processed, and if you want to be at the head of the line then you should include a transaction fee.
Where do "I can't see my unconfirmed transaction" delays come from?
- If the sender is bunching transactions to save on TX fees.
- If the sender uses an air-gap system for security, slowing the speed that transactions reach the p2p network.
- If the sender hasn't sent them yet.
- p2p network propagation delay (this is fast, less than 5 minutes if you are well connected.)
Where do "My transaction isn't confirmed" delays come from?
- Miners preferring to process transactions with a higher (non-zero) TX fee.
- Miners ignoring Double-spend transactions.
Big takeaway: Include a transaction fee on your transactions, then the miners will prefer your transactions and confirm them faster.
* - * cough* satoshi dice *cough*