That's great,
What i don't understand is, the blockchain,
Why does bitcore client need the blockchain, and electrum doesnt need the blockchain.
In fact, i am now very confused, What exactly is the purpose of the blockchain, and why doesnt electrum need it
Bitcoin Core is a full node. This means that it fully verifies and validates every single transaction and block that it receives. In order to do that, it must know the entire history due to the chaining, so it must download the entire blockchain. Actually, with 0.12, while it still needs to download the entire blockchain, if pruning is enabled, it does not need to store the entire blockchain.
Electrum (and many other wallets like MultiBit) is an SPV wallet. This means that it relies on someone else to provide it the proper information. SPV wallets rely on full nodes to validate the transactions and blocks and then the wallet requests only the information that is relevant to it. It is unable to fully validate and verify blocks and transactions because it does not have the full history. This means that SPV nodes are slightly less safe because you need to trust someone else to provide the right information. In general, SPV wallets are still very safe.