Recently I read a good article from www. whoishostingthis.com/blogs. It explains what Bitcoin is and tells you how you could explain it to your grandparents. Below I consolidated the info and added some of my own in MY own understanding of what Bitcoin is:

What is Bitcoin ? * Bitcoin is a digital global money system (currency). It allows you to send or receive money across the Internet. The mathematical field of cryptography is the basis of Bitcoin's security. * It's Decentralized which means that no one particular party owns it. * You can buy products on the Internet or cash it in for local currencies. There are now 15,000 retailers online (plane tickets, furniture, Dell computers, Amazon gift cards). * Bitcoin can be bought through online Exchangers using a credit card or bank draft. (You can also buy physical Bitcoins which come with an encrypted code if you want). * Bitcoin is stored in a digital "Wallet" (just like a bank account without a bank). Wallets can be stored on a website, on your computer alone, on a cell phone, a device, or even on paper. (all cryptographically password protected) * A digital Wallet contains: online Bitcoin addresses and a private key (a big long alpha numeric password). Bitcoin addresses: They are like a bank account number. You may have 4 or 5 or more in your Bitcoin wallet. Each address (like a bank account #) has a balance. The balance could be from $0 to a million or 50 million or whatever. Private Key: a secret code (like a PIN #) is generated for each address (bank account#) where you hold your Bitcoin. There is only one secret code and only the user knows it. * Spend Bitcoin online or at a local retailer (I recommend you only put into your phone wallet what you plan to spend - like cash in your wallet). Example: Go to subway(some in California accept Bitcoin) or a shop (that excepts Bitcoin) scan the QR code on the bill they give you and then send to the Subway or store's Bitcoin address. * The transaction is processed on an open digital ledger called the Blockchain network. It is processed by miners (all over the world on thousands of computers). *Everyone sees the transaction and address, but NOT your Private Key, your bitcoin balance, or your personal data. * The transaction is encrypted = turned into an alpha numeric code. Then it is included with other transactions in a "Block". Thousands of miners work to verify it. Miners receive 25 Bitcoins for verifying/solving a block. This ensures that no Bitcoin is ever spent twice, no Bitcoin is hijacked, and no personal date is exposed - unlike a credit card transaction. * There are a limited amount of Bitcoins(21 Million). They will not all be in circulation until around the year 2140. * The cost/fee for a transaction by miners over the blockchain is between 0 and 1 cents (USD). The cost to send Bitcoin overseas through the internet is almost nothing. Western Union and other remittance agencies charge average of 2 to 3 %. Remittance is a multi-billion Dollar industry. International immigrants are sending $500 Billion dollars a year back to fmaily members in their respective countries. * Is it real ? US Citizens must pay the IRS taxes on all Bitcoin capital gains. It's real enough for the IRS to tax it ! It's as real as the money in your bank but it's acceptance is not universal yet. * Can you buy groceries with it ? Not just yet, but it's probably a matter of time (although you can buy them with a debit card linked to your Bitcoin account). * Is it Safe ? A Bitcoin transfer can be safer than a credit card transaction as it doesn't involve personal credit card data. * There are currently 740 types of crypto-currencies but only 24 - 26 of them have a market capitalization of over $10 Million.