Hi Steemit-Community, I am ManonLescaut and this is my first post ever. I will explain the concept of „Digital Signatures“ in Bitcoin-Payments and how they assure that only you, as the only legitimate holder of your Bitcoin, are able to spend them. My Supergirl @RatzFratz ( is waiting for Account-activation 15th. July :D) created the graphics with love for you! I would appreciate any honest critic. Thanks
So lets imagine you are a merchant who sells some goods. You accept two currencies in your store, US-Dollar and Bitcoin. 
So as you will receive these two currencies you need something where you can store the accepted US-Dollars and Bitcoins. For the US-Dollar you go to a shop around the corner and buy a normal wallet, where you can put in the cash. For storing your Bitcoins you are not buying an actual wallet like the one for US-Dollar, you are downloading a free digital wallet, lets call it „BitcoinWallet“ on your computer. Imagine it like a real wallet, just in digital form. For better understandings, lets imagine a normal envelope as your digital Bitcoin-Wallet, you just downloaded. 
When the Bitcoin-Wallet is downloading, on a technical level what is happening, is that the wallet is being generated by the software. In terms of our Bitcoin-Wallet envelope analogy, the software starts with generating the left-side of the envelope. We call this left side the „private key“. This „private key“-left side envelope is unique. That means there is no other left-side of an envelope that looks like yours. The blue pattern on the edge of the envelope illustrate its uniqueness. We will see in a second why this is important. (I will explain in an later article what mathematical function assures, that the envelope is unique).
After, the left-side of the envelope was created, the software starts to create the right-half of the envelope. The right-half is called „public key“. This right-side is not randomly created though. It is being generated from the unique private-key-left-side envelope. So, both halves fit together.
So your Bitcoin wallet consists of these two halves of the envelope; The „private key“-left-half and the „public key“-right-half.
You keep the „private key“-left-half envelope very safe and hidden. As the name of it implies, this left-half-envelope is private and only you should have access to it. It’s important to no tell anyone about it. It is your secret. Next you take your real world wallet for US-Dollar and the „public key“-right-half envelope and go to your shop. Now two buyers come into your shop. Buyer 1 purchases some goods and wants to pay with US-Dollars. He is handing out US-Dollars to you. You are pointing to your real-world wallet on the cash desk and tell Buyer 1 to put the cash into that wallet. Now Buyer 2 wants to pay for the goods with Bitcoin. You pointing to the „public key“-right-half envelope on the cash desk and tell Buyer 2 to put the Bitcoin into it.
Now you have the real wallet with US-Dollars from Buyer 1 and your „public key“-right-half envelope with Bitcoins from Buyer 2.
What are you doing next? You take the wallet with US-Dollars and the „public key“-right-half envelope with Bitcoins, put them on the street and leave.
Soon a pedestrian walks by. He notices the left-behind wallets and stops. He picks up the real wallet and takes it with him. Afterwards he leaves, without even touching the „public key“-right-half envelope with the Bitcoins in it.
Why is he taking the US-Dollars? He takes the US-Dollars, because he can go with them to the next shop and purchase some goods with it. Why is he not taking the „public key“-right-half envelope with Bitcoins? It is not because the Bitcoins have no value. But because, these specific Bitcoins on the street don’t give the pedestrian any purchasing-power. The reason is, that the Bitcoins (from Buyer 2) are attached to your „public key“-right-half envelope, and they can not be taken out. You may question here: „How about if the pedestrian just takes the „public key“-right-half envelope with the attached Bitcoins and tries to spend them attached together, maybe it is not necessary to take the Bitcoins out of the right-half envelope? Well, here is where one of the key points of Bitcoin-technology comes into the game. The reason why the pedestrian is ignoring the Bitcoins on the street is, that a „public key“-right-half envelope can only receive Bitcoins. That’s its only function. That is the reason why you can make the right-half-envelope public. The only thing people can do when they have your „public key“-right-half envelope, is putting more Bitcoins into it. Nobody can take it out, not even you. Once in, the Bitcoins are attached to the „public key“-right-half envelope forever. The only way to spend these Bitcoins is to add the unique paring „private key“-left-half envelope, which (remember) the „public key“ was generated from. In other words: Bitcoins can only be spent if they come in a full and gapless envelope, which consists of the „private key“-left half and the „public key“-right half of the envelope. That means, everybody accepts only Bitcoins which are enclosed by a full complete envelope, where both halves fit gapless to each other.
So, when I talked about Buyer 2 who paid you in Bitcoins, he actually put a full, gapless envelope (consists of left-side and the matching right-side envelope) with Bitcoins (actually another full envelope Buyer 2 received before) in it, into your „public key“-right-half envelope.
Back to our story. In the next morning you are going back to the place where you left your US-Dollars and Bitcoins on the street, and notice that your Dollars are gone but the right-half-envelope with the Bitcoins from Buyer 2 is still there, as nobody except you (who is the only holder of the matching „private key“-left-side envelope) is able to make a full, gapless envelope. You take the „private key“-left-half envelope, which you hidden before and add it to the right-half-envelope where the full-envelope of Buyer 2 is attached to. Now the full-envelope with Bitcoins from Buyer 2 is in a full-envelope again and can finally be spent.
The fact that you can provide the unique „private-key“-left-half envelope which is the only left-side that fits gapless to the „public key“-right-half envelope, proves that you are the creator of the „public key“-right-half envelope. That means, all Bitcoins which are attached to this right-half envelope (e.g. Bitcoins from buyer 2) belong to you.