Consider gold. Gold occupies a specific point in space. A gold coin cannot exist in multiple points simultaneously. I cannot store a gold coin at my house and store that same gold coin in my bank deposit box. Gold also has density. I cannot transport one million dollar's worth of gold through airport security because it would weigh over 40 pounds and would be easily picked up by a metal detector. To transport one million dollar's worth of gold from New York to Berlin, one would have to pay for international shipping, and the total cost would be over $300, and that's a conservative estimate(1). For larger amounts, such as the transfers of several billion dollars' worth of gold to Fort Knox, operations to build gold vaults cost millions of modern-day dollars. It can also be inferred that millions of dollars are spent every year on guards and maintenance, which is necessary to store over 4,000 tons of gold. Gold can be sold in large amounts, but transportation can be expensive. Gold is mined by many different companies, and it is universally acknowledged as a store of value. Stealing large amounts gold can be tricky because of it's bulk, but overall, it's easy to move around relatively small amounts.
Now let's consider cash. Cash, like gold, cannot exist in multiple locations, because it occupies a definite point in space. It can be treated very similarly to gold in that it costs large amounts of money to secure. One difference, however, is that central banks have the power to essentially print as many banknotes as they want(3). This creates risk that a third party may cause high inflation or engage in currency manipulation. Banknotes are accepted at nearly every merchant within their jurisdiction. However, in order to spend banknotes outside of the original jurisdiction, one must convert them to foreign currency. Banknotes, like gold, must be stolen physically, and depending on the denomination stolen, the value per pound of banknotes may or may not be worth the effort to steal. Cash can be traced through serial number(4), although this is difficult. Transporting cash is also expensive, although this can be alleviated by converting it into digital fiat.
Digital fiat currency can be found in bank accounts, on stock markets, on Paypal, on credit cards and in the form of gift cards. Digital fiat is unique because several people can own it at the same time. For example, If I buy a $100 visa gift card and share the code with my friend, which of us owns that money? Most would argue that it's whoever can spend it first. Digital fiat currency has become increasingly easy to steal through fraud (5) and hackers have been hard at work. Use of digital fiat also required trust in a third party. Digital fiat service providers have become notorious for freezing user accounts upon government request, and even if a user's transactions look suspicious. Fees are also high with digital fiat, and there are many government barriers to using it internationally. Anti- money laundering laws in many countries make it extremely difficult to use digital fiat.
Finally, look at bitcoin. Bitcoin requires no third party trust, and, provided you own the private key, nobody can take your bitcoins away from you. The private key is a short string of numbers and letters, meaning that once the corresponding address receives value, that short string itself has value. Isn't that an amazing concept? Bitcoins can also exist in many points in space simultaneously. For example, I could print out a private key and store 20 copies in different locations, and they would exist at each place at the same time. Bitcoin is also unique in that multi signature wallets can be arranged, where a specific number of shareholders must collaborate in order to spend value. In that regard, bitcoin exists in a "limbo state" until it is spent. Bitcoin can also be used to verify that a piece of data is an authentic copy, or to upload a message or data onto the blockchain. Bitcoin is also not a physical thing, meaning that sending 100 million dollars could cost the same as sending 5 dollars. Compare this to gold and cash, which are bulky things. The supply of bitcoin is cut off at 21 million coins, so there is no chance of unexpected inflation occurring. Bitcoin, like gold, is universal, in that a bitcoin in China is the same as a bitcoin in Brazil. In short, bitcoin is a revolutionary new way to store value.