"Understand the why before you understand the what"

To understand why do we need Bitcoin, we need to understand what is wrong with money nowadays. To understand that we need to remember who we are now and who we were at the beginning.

The History of money:
At the very beginning, we as a civilization had no type of money. The only way of buying food or clothes was barter. Some meat for a fresh bread, warm bear's skin for a spear or a few cows for a house. It was not practical, either universal. There was a need for a utilitarian medium of exchange, so the currency was born. We used shiny rocks, seashells and many other items.
And what connects all of them? THEY WERE DECENTRALIZED. There was no mint or factory behind seashells. If you were lucky or smart enough there was a chance of finding them on a beach.
Next, some authority convinced people that metal circles are better in use than rocks (which obviously is true). The same authority decided that the supply of coins should be in his hands, so no one was able to fake their currency. It was the first centralization of money. Things lasted like this for thousands of years, until gold came in the game...
The supply of gold was once again decentralized, and (once again) if you ware lucky enough there was a possibility of finding some in a river or underground. Gold has also one more advantage over other metals like copper. It is more or less hard capped. This means there is a limited amount of it (not saying that cooper is unlimited ofc). For many years alchemists were (and probably still are) trying to synthesize gold but still, it's not possible. It was a fair currency and that is probably the reason it is the longest existing type of money. But trading heavy gold bars is not practical at all.
History likes to repeats itself so again some authority decided to take control over it. At the beginning the idea was great. Gold was melted into coins and coins were easier to use. Here happened the second centralization.
IMG NOT FOUND Later the bills were invited. They (the executive power) promised us that every piece of paper will have some amount of gold stored safely by the government. The "Gold Standard" was born. Until 1971 we believed that notional currencies are backed. The man who changed everything was 37th POTUS* (Richard Nixon). Then the "Nixon shock" have occurred and FIAT's were born (FIAT is a currency backed by nothing at all). The rule that USD needs to be backed by the equal amount of gold was just erased and governments started printing money like it was a toilet paper. Somehow they managed to convince people that these currencies have value.
Just to stay historically precise: the oldest FIAT currency was not invented in the USA, but in China. One thousand years earlier. France also did it one year before the USA.
These days it is not even about printing money, it became nonsense. Governments are just adding numbers to their bank account. No one controls that (government being controlled by themselves is just ridiculous).

The money we use is evolving just like all other things in this world, but money evolution is repeating itself. Sometimes it's decentralized and uncontrolled and other times it becomes dependent and centralized. Money is the best way of exchanging value (so far), but the idea of someone managing it is not necessary neither good for the rest of us. The ruler always undergoes the desire of having more of it (human psychology just works like that).
We have never had a type of money that was resistant to any centralized control, until BITCOIN was born.
There are some who believe that it could possibly be controlled ( 51% attack or the world without internet). Let me crush these ridiculous arguments.
The attempt of generating such a computing power to take over 51% of BTC hash rate is unbelievably hard but theoretically possible. Current HR (hashrate) is 57,854 PH/s (still increasing) so owning just a bit more than half of it for one hour will take a lot of effort. Let's assume that some government wishes to do so, they could use the citizen's hardware and possibly achieve that. And then what? Taking control over the network will just destroy it (no matter what the overtaker wants to do). What's the point of controlling something that does not work? Another thing to keep in mind is that BTC will be only mined till 2140 (not so far if you think how long an adoption could take), then no one will care about mining.
Another "danger" is the internet shutdown. Ignoring the fact how hard it is and the worldwide chaos, manifestations (probably even anti-government rebellion) it will cause. BTC uses the internet only because its the most accessible, cheapest, fastest and widest network currently existing, but it is not the only one. Offline transactions are already possible and the internet could be easily replaced by GSM or even old-school pigeons. No threat for BTC here.

BTC is the first currency that just cannot be centralized. It was designed for that. Starting from cypherpunks in 70's, evolving through many imperfect creations and ending with Satoshi's publication. They were all working for that one purpose.

Humanity was born decentralized. Separating in centralized societies is unnecessary (and stupid). Greeks invented a democracy (decentralized way of administration) and Satoshi invented blockchain. This gave us the decentralized type of money. Now we only need to understand this and become one global community.