From a widespread adoption standpoint: for the typical consumer, Bitcoin is technically challenging and cumbersome to use for the inexperienced. They also forfeit the consumer protections afforded by traditional credit and debt cards. Merchants already have incentive to accept it in the form of reduced fees for accepting payments over typical payment processors.
Though it is tempting to believe the media's spin that Satoshi Nakamoto is a lone, quixotic genius who created Bitcoin out of thin air, such innovations do not happen in a vacuum. All major scientific discoveries, no matter how original-seeming, were built on previously existing research. There are precursors to Bitcoin: Adam Back’s Hashcash, invented in 1997, and subsequently Wei Dai’s b-money, Nick Szabo’s bit-gold and Hal Finney’s Reusable Proof of Work. The Bitcoin white paper itself cites Hashcash and b-money, as well as various other works spanning several research fields.

Nor was it simply the deep pockets. At these prices, even smaller operators have been able to make real money running a few machines in home-based, under-the-radar mines. Take the 20-something Wenatchee man we’ll call “Benny”—he didn’t want to be identified—who last July bought three mining servers, set them up in his house (one in the master bedroom and two in the living room)—and began mining Ethereum, bitcoin’s closest cryptocurrency rival. As Ethereum climbed from $165 in July to nearly $1,200 in January, Benny had not only repaid his $7,000 investment but was making enough to pay his mortgage. As a side benefit, this winter, Benny’s power bill went down: The waste heat from the three churning servers kept the house at a toasty 78 degrees. “We actually have to open the windows,” he told me in January. His servers, meanwhile, pretty much run themselves—although, when he’s at work, clerking at a grocery, he monitors the machines, and the Ethereum price, on his phone. “It’s just basically free money,” Benny says. “All I have to do is wake up in the morning and make sure nothing crashed during the night.”
The other reason is safety. Looking at 2009 alone, 32,489 blocks were mined; at the then-reward rate of 50 BTC per block, the total payout in 2009 was 1,624,500 BTC, which at today’s prices is over $900 million. One may conclude that only Satoshi and perhaps a few other people were mining through 2009, and that they possess a majority of that $900 million worth of BTC. Someone in possession of that much BTC could become a target of criminals, especially since bitcoins are less like stocks and more like cash, where the private keys needed to authorize spending could be printed out and literally kept under a mattress. While it's likely the inventor of Bitcoin would take precautions to make any extortion-induced transfers traceable, remaining anonymous is a good way for Satoshi to limit exposure.
In the blockchain, bitcoins are registered to bitcoin addresses. Creating a bitcoin address requires nothing more than picking a random valid private key and computing the corresponding bitcoin address. This computation can be done in a split second. But the reverse, computing the private key of a given bitcoin address, is mathematically unfeasible. Users can tell others or make public a bitcoin address without compromising its corresponding private key. Moreover, the number of valid private keys is so vast that it is extremely unlikely someone will compute a key-pair that is already in use and has funds. The vast number of valid private keys makes it unfeasible that brute force could be used to compromise a private key. To be able to spend their bitcoins, the owner must know the corresponding private key and digitally sign the transaction. The network verifies the signature using the public key.[3]:ch. 5
Transactions are defined using a Forth-like scripting language.[3]:ch. 5 Transactions consist of one or more inputs and one or more outputs. When a user sends bitcoins, the user designates each address and the amount of bitcoin being sent to that address in an output. To prevent double spending, each input must refer to a previous unspent output in the blockchain.[67] The use of multiple inputs corresponds to the use of multiple coins in a cash transaction. Since transactions can have multiple outputs, users can send bitcoins to multiple recipients in one transaction. As in a cash transaction, the sum of inputs (coins used to pay) can exceed the intended sum of payments. In such a case, an additional output is used, returning the change back to the payer.[67] Any input satoshis not accounted for in the transaction outputs become the transaction fee.[67]

Bitcoins can be accepted as a means of payment for products sold or services provided. If you have a brick and mortar store, just display a sign saying “Bitcoin Accepted Here” and many of your customers may well take you up on it; the transactions can be handled with the requisite hardware terminal or wallet address through QR codes and touch screen apps. An online business can easily accept bitcoins by just adding this payment option to the others it offers, like credit cards, PayPal, etc. Online payments will require a Bitcoin merchant tool (an external processor like Coinbase or BitPay). 
The Bitcoin network shares a public ledger called "blockchain". This ledger contains every transaction ever processed, allowing a user's computer to verify the validity of each transaction. The authenticity of each transaction is protected by digital signatures corresponding to sending addresses, allowing all users to have full control over sending Bitcoins from their own Bitcoin addresses. In addition, anyone can process transactions using the computing power of specialized hardware and earn a reward in Bitcoins for this service. This is often called "mining".
In January 2009, the bitcoin network was created when Nakamoto mined the first block of the chain, known as the genesis block.[18][19] Embedded in the coinbase of this block was the following text: "The Times 03/Jan/2009 Chancellor on brink of second bailout for banks."[10] This note has been interpreted as both a timestamp and a comment on the instability caused by fractional-reserve banking.[20]:18