Can someone shed some light on what it I actually receive when I purchase a bitcoin and how I can verify that what I have 'in my hands', is actually a bitcoin and not just a bunch of ones and zeros? I understand that the blockchain is supposed to verify what is what but, what if I wanted to pass my bitcoin directly to you without the blockchain. Again, how would I know, what I received - was a bitcoin?
You can't make a fake Bitcoin and even you can create fake transaction, network will definitely reject it, and you can't create new Bitcoin without having 51% of Bitcoin mining hashing power. So if you receive Bitcoins in your Bitcoin wallet it is surely an authentic one, or if you are still not satisfied, you can copy the transaction ID of your transaction and paste it on block explorer, if you can see that your Bitcoin is recorded there or the transaction status is confirmed then it is real. It is impossible for anyone to transfer Bitcoin without blockchain because all transactions are recorded in blockchain, unless you give the ownership (private key) of your Bitcoin wallet to other people, that's the only possible way to transfer Bitcoin without creating a transaction.