What is the coin sweep thing?
Importing basically inserts your private key into a wallet (NOTE: this isn't possible with HD wallets, you can't insert foreign private keys)... so the coins stay under the control of the existing private key.
Sweeping, creates an "on-chain" transaction and sends the coins from the address of the existing private key to a brand new address (and matching private key). Usually this is done when you're wanting to either "burn" the private key and never use it again and/or to get the coins into an HD wallet when they're coming from a "random private keys" type wallet (ie. older non HD wallets, paper wallets, brain wallets etc)
Watch addresses = People who use air-gapped offline computers to hold their private keys and sign transactions but need a way to see all the coins in certain addresses... (and/or nosey people who want to watch addresses for transaction activity)
I'm clueless. lol How does that work?
For added security, you create an "offline" wallet. This is done on a computer that never has (and never will) be on a network... hence the term "air gapped". It has no network connections. You create your wallet and private keys...
Then on a separate, internet connected computer... you create a "watching only" wallet that has the same addresses, but no private keys (without private keys, you can only view the contents of addresses, you cannot spend any coins)...
When you want to send coins, you create an "unsigned" transaction on the online PC... transfer it (usually via USB) to the offline PC... "sign" the transaction with the private keys... transfer the "signed" transaction back to the online PC and broadcast it to the network.
In theory, this should prevent your private keys ever being compromised unless someone has direct physical access to the offline PC.
http://docs.electrum.org/en/latest/coldstorage.html